Short Presentations

A Comparison Between Two Non-Linear Optimization Methods for Seismic Ray Tracing on Complex 3D Heterogeneous Geological Media
A New Fast “General Ray” Method for Solution of Boundary Problems for Partial
Differential Equations
A Numerical Method for Three Dimensional Void Electromigration
A Parallel Simulator of Framed Structures
A Remark on the Stability of Solitary Waves for 1-D Benney-Luke Equation
A Tridimensional Study of the Kerogen Maturation Process in Evolutionary Basins
Basic Properties of Unstable Normal Modes of Steady Ideal Flows on a Rotating Sphere
Constructing Accurate Polynomial Approximations for Nonlinear Differential Initial Value Problems
Constructing Mean Square Discrete Solutions for Random Differential Equations
Displacement of Immiscible Fluids in Porous Media
Eigenvalues of Linear Operators and its Approximations
Fast Computation of Equispaced Pareto Manifolds and Pareto Fronts for Unconstrained Multi-Objective Optimization Problems
FGMRES Preconditioning by Symmetric-Antisymmetric Decomposition of Generalized Stokes Problems
Fuzzy Ant Colony Optimization for Estimating the Chlorophyll Concentration Profile in Offshore Sea Water
Heisenberg's Turbulent Spectral Transfer Theory for Sub-grid Parameterization in LES Models
High Order Adaptive Finite Difference Schemes for Maxwell's Equations
Inferring the Left Ventricle Dynamical Behavior Using a Free-Form Deformations Model
Mimetic Discretization of Elliptic PDE Problems With Full Tensor Coefficients
Multiresolution Based Grid Coarsening for Discontinuous Problems
Multiscale Analysis by Discrete Mollification
Nonstandard Methods for More General Reaction Terms
Numerical Modeling of Hydrodynamic Processes Forced by Wind and Tide in the Paracas Bay Pisco-Perú
Numerical Simulation of a Degenerate PDE Model for the Formation of TCE Degrading Dual-Species Biofilms
Numerical Solution of Test Neutral Functional Differential Equations with the Segmented Formulation of the Tau Method
Numerical Treatment of an Inverse Problem for a Strongly Degenerate Parabolic Equation
On a Method for Constructing the Shallow-Water Discrete Models Conserving the Total Mass and Energy
On Generation of Conformal Mappings of Spherical Domains
On the Parameter Selection Problem in the Newton-ADI Iteration for Large Scale Riccati Equations
Optimal Power Split in a Hybrid Electric Vehicle Using Direct Transcription of an Optimal Control Problem
Optimization of Solar Low Energy Building Design
Orthogonal Polytopes Modeling Through the Extreme Vertices Model in the n-Dimensional Space
Out-of-Core layer of UCSparseLib
Parameter Identification of Nonlinear Dynamical Models by Using Differential Evolution Algorithms

Preconditioning Techniques for Saddle Points Problems

Sphere Inversion and 3D Lemniscates Singularities
The Method of Meshless Fundamental Solutions for the Pressure Equation in Oil Field Problems
The Simulation of The Circulation in Todos Santos Bay, Mexico
Transformation Algorithm of a Matrix that Determines the Stability in Square Mean of a Dynamical Input-Output System
Two New Algorithms for the Joint Replenishment Problem
Water Uptake by Root of Croops: A Moving Boundary Approach

A Comparison Between Two Non-Linear Optimization Methods for Seismic Ray Tracing on Complex 3D Heterogeneous Geological Media

Aldo Reyes-Cortez
areyes@uc.edu.ve

Rina Surós
rsuros@cantv.net

Abstract: Travel time inversion allows to recover elastic properties of rocks from seismic measurements made on the surface of the earth, the bottom of the sea or in deep wells. Ray tracing methods are used in order to simulate the forward problem of calculating ray paths between each source-receptor pair and then computing the travel times and wave amplitudes. In this work we propose and implement an algorithm for seismic ray tracing in complex 3D heterogeneous geological media. We consider complex geological models conformed by a coherent ensemble of irregular rock bodies limited by explicit surfaces. In this approach the blocky model is interactively created by defining elemental topological operations on the initial layered media as is usual in computer aided design systems. The requirement of ray tracing algorithms for smooth second derivatives is guaranteed by building a set of parametrical surface patches that smooth interconnect. This approach permits the modeling of such geological characteristics as folded layers, inclusions, faults and overthrust. The ray path is modeled by a piecewise cubic between block interfaces. We use then a bending strategy guided by and optimization algorithm to find, between each source-receptor pair, the ray path with minimum travel time. We present experimental results obtained by using and comparing the Barzilai and Borwein optimization method modified by M. Raydan (GSG) and the circular Barzilai and Borwein (CBB) from Y. H. Dai.


A New Fast “General Ray” Method for Solution of Boundary Problems for Partial
Differential Equations

Alexandre Grebennikov
agrebe@fcfm.buap.mx

Abstract: A new approach for solution of the boundary problems for a wide class of partial differential equations of mathematical physics is proposed. This class includes the Laplace, Poisson, Helmholtz and parabolic equations. The approach is based on the Local Ray Property discovered by the author and leads to a new General Ray (GR) Method, which presents the solution of the Dirichlet or Neumann boundary problems by explicit analytical formulas with the inverse Radon transform. GR-Method is realized by fast algorithms and MATLAB software, and its quality is demonstrated by numerical experiments.


A Numerical Method for Three Dimensional Void Electromigration

Lubomir Banas
l.banas@imperial.ac.uk

Robert Nurnberg
robert.nurnberg@imperial.ac.uk

Department of Mathematics
South Kensington Campus
Imperial College London
London

United Kingdom

Abstract: We study a numerical method for a three dimensional phase-field model for void electromigration by surface diffusion in electrically conducting solids. The corresponding problem in two dimensions has been studied in [1]. The model consists of a degenerate Cahn-Hilliard equation coupled with a degenerate Laplace equation for the electric field. We prove convergence, and hence existence of a solution in three space dimensions. We present some numerical experiments in 3D. In addition to [1], where only space adaptivity is employed, we present a space-time adaptive algorithm.

References
[1] J.W. Barrett, R. Nurnberg, and V.Styles, Finite element approximation of a phase field model for void electromigration, SIAM J. Numer. Anal., 42 (2004), pp. 738--772.


A Parallel Algorithm for Seismic Modeling

German Larrazabal
glarraza@uc.edu.ve

Aldo Reyes
areyes@uc.edu.ve

CEMVICC - FACYT
Valencia, Estado Carabobo, Venezuela

Abstract: In this work, we present an asynchronous parallel algorithm for seismic modeling. This algorithm solves the two-dimensional acoustic wave equation for heterogeneous media using a finite difference technique. We have used a message passing model to exploit parallelism. An efficient asynchronous communication between processes has been implemented. For the tests, we have generated different velocity models using the 3D UC-geoModel tool and we also use the Marmousi benchmark. We have obtained a high scalability and good numerical results on a Sun Cluster machine with 16 dual Opteron processors.


A Parallel Simulator of Framed Structures

Richard Espinoza
richardg@ula.ve

Julio Florez
iflorez@ula.ve

German Larrazabal
glarraza@uc.edu.ve

Faculty of Engineering
CIMA, Los Andes University
Merida, Venezuela

Abstract: In this work, we present a new parallel simulator of framed structures. This simulator is an finite element program based in concepts of lumped damage mechanics to simulate planar frames. This program allows the analysis and numerical simulation of reinforced concrete frame structures under earthquakes or other exceptional overloads. We use OpenMP library to exploit the parallelism on share memory machine or share-distributed memory machine. The results obtained show the good performance of the simulator.


A Remark on the Stability of Solitary Waves for 1-D Benney-Luke Equation

Eduardo Ibarguen Mondragón
edbargun@udenar.edu.co

José Raúl Quintero
quinthen@univalle.edu.co

Universidad de Nariño
Departamento de Matematicas y Estadistica
Ciudad Universitario Torobajo, San Juan de Pasto, Colombia

Abstract: The aim of this work is to analyze the stability of the solitary waves of the one-dimensional Benney-Luke equation. We will prove that the null solution is asymptotically stable due to the presence of the Hamiltonian structure and to the existence of invariant quantities with regard to the time. In the case of the solitary wave not null, we found the Hamiltonian structure but the verification that some quantities are conserved with respect to time have turned out to be a difficult numeric calculation. We show that the criteria of stability and orbital instability of M. Grillakis, J. Shatah and W. Strauss is not applicable and we present numeric results of unstable solitary waves. WebPage : http://www.univalle.edu.co/~quinthen


A Tridimensional Study of the Kerogen Maturation Process in Evolutionary Basins

Elbano David Batista Pérez
numerico@gmail.com

Oswaldo J. Jiménez
oswjimenez@usb.ve

Universidad Simón Bolívar
Dpto de Cómputo Científico y Estadística
Sartenejas - Baruta, Venezuela

Abstract: It is presented a three dimensional simulation of the organic matter maturation process. The organic matter or kerogen is placed in sedimentary basins which geological structures change during the geological time because of the action of compressive tectonic forces. These structures consist, basically, of two blocks, the allocthone block and the autocthone block, separated by a fault plane. The allocthone block overthrusts the autocthone one following a simplified "fault-bend fold" kinematical model. The temperature of the basins, one of the most important factors in the kerogen maturation process, is obtained by an external numerical model based on the finite element method. The integrals quantifying the amount of kerogen potentially transformable into hydrocarbon are calculated using the temperature on the basins along with some rational approximations. The results obtained in this work show the dependence of the kerogen maturation speed on the organic matter type. Also, it is detected an important variation in the maturation index at different locations along and across the basin, mainly on the structures having a more realistic 3D profile, thus showing the necessity of modeling the maturation process in 3D rather than in 2D.


Basic Properties of Unstable Normal Modes of Steady Ideal Flows on a Rotating Sphere

Yuri N. Skiba
skiba@servidor.unam.mx

Centro de Ciencias de la Atmósfera
Universidad Nacional Autónoma de México
Ciudad Universitaria, México, D.F., México

Abstract: A unified approach to the normal mode instability study of exact steady solutions to the vorticity equation governing the motion of an ideal incompressible fluid on a rotating sphere is considered. The four types of the solutions known up to now are considered, namely, the Legendre-polynomial (LP) flows, Rossby-Haurwitz (RH) waves, Wu-Verkley (WV) waves and modons by Verkley and Neven. Conservation laws for infinitesimal perturbations to each of these solutions are derived and used to obtain necessary conditions for their exponential instability. By these conditions, Fjörtoft's (1953) average spectral number of the amplitude of an unstable mode must be equal to a special number. In the case of the LP flows or RH waves, this number depends only on the solution degree. For the WV waves and modons, it depends both on the solution degree and on the spectral distribution of the mode energy in the inner and outer regions of the solution. Peculiarities of the instability conditions for different types of modons are noted. For the LP flows, the new instability condition refering to the spectral structure of growing disturbances complements the well-known Rayleigh-Kuo condition related to the basic flow structure. The new instability conditions localize the unstable disturbances in the phase space, are useful in interpreting the spectral structure of growing atmospheric perturbations and in testing the computational algorithms designed for the exponential instability study. The maximum growth rate of unstable modes is estimated, and the orthogonality of any unstable, decaying and non-stationary mode to the basic solution is shown. These results can also serve as good tests for the computational programs used in the numerical stability study. Note that the maximum growth rate estimates have also been obtained through the Fjörtoft's spectral number. Thus, we can say that this number is the key parameter of the linear instability problem.


Constructing Accurate Polynomial Approximations for Nonlinear Differential Initial Value Problems

 

María Dolores Roselló Ferragud
drosello@imm.upv.es

Lucas Jódar Sánchez
ljodar@imm.upv.es

B. Chen
bchen@uwyo.edu

R. Company
rcompany@imm.upv.es

Instituto de Matemática Multidisciplinar, Edificio 8G, 2
Universidad Politécnica de Valencia
Valencia, Spain

Abstract: This paper deals with the construction of a polynomial approximate solution with a prefixed accuracy, of initial value problems for nonlinear ordinary differential equations. By approximating the right-hand side of the equation by an appropriate two-variables Chebyshev polynomial and by truncating a further application of the Frobenius method, a polynomial approximate solution is constructed. Recent results of [1] and [2] are improved in two directions, by extending the existence domain of the approximation and by reducing the truncation polynomial degree.

References
[1] B. Chen, R. García Bolós, L. Jódar, M.D. Roselló, The truncation error of the two-variable Chebyshev series expansions, Comput. Math. Appl., 45 10-11, pp. 1647-1653 (2003)
[2] B. Chen, R. García Bolós, L. Jódar, M.D. Roselló, Chebyshev Polynomial Approximations for Nonlinear Differential Initial Value Problems, Nonlinear Analysis, 63 5-7, pp. e629-e637 (2005)


Constructing Mean Square Discrete Solutions for Random Differential Equations

Laura Villafuerte Altúzar
lva5@cimat.mx

Lucas Jódar
ljodar@imm.upv.es

Juan Carlos Cortés
jccortes@imm.upv.es

Instituto de Matemática Multidisciplinar
Universidad Politécnica de Valencia
Valencia, Spain

Abstract: This paper deals with the construction of discrete mean square approximating processes of initial value problems for random differential equations. We are mainly interested in the computation of the expectation E [Xn] and variance V [Xn] of the approximating process Xn. Convergence conditions and illustrative examples are included.


Displacement of Immiscible Fluids in Porous Media

María del Carmen Hernández Rendón
carmen.hernandez@inegi.gob.mx

Abstract: In this work, a numerical model to simulate two phase flow in porous media is described and analyzed. The main feature of the procedure presented here is the use of the Trefftz-Herrera collocation method to approximate spatial derivatives. To define primary variables, a factional flow formulation of the problem is employed. In order to illustrate some advantages of this method, numerical results are displayed and discussed for different test cases.


Envelopes and Tubular Splines

Paluszny, Marco
marcopaluszny@gmail.com

Tovar, Francisco
ftovar@euler.ciens.ucv.ve

Universidad Central de Venezuela
Laboratorio de Computación Gráfica y Geometría Aplicada
Caracas, Venezuela.

Abstract: Envelopes of 1-parameter families of spheres determine canal surfaces. In the particular case of a quadratic family of spheres the envelope is an algebraic surface of degree four that is composed of circles. We are interested in the construction of smooth tubular splines with pieces of envelopes of quadratic families of spheres. We present schemes for the interpolation of a sequence of circles in 3D and more generally, of circle contacts (i.e. sequences of "circles on spheres" pairs such that the spline contains the circles and is tangent to the sphere). We compare heuristics for the generation of default tubular splines for prescibed circular contacts.


Eigenvalues of Linear Operators and its Approximations

Slavisa Djordjevic
slavdj@fcfm.buap.mx

Facultad de Ciencias Físico-Matemáticas
Puebla, Puebla, Mexico

Abstract: In this note we consider eigenvalue problem for operators on infinite dimensional Banach space. Exact eigenvalues, eigenvectors, and generalized eigenvectors of operators with infinite dimensional rang can rarely be found. It is imperative to approximate such operators with operators that belong to some well-known class of operators such as finite range operators or normal operators, and solve the original eigenvalue problem approximately.


Fast Computation of Equispaced Pareto Manifolds and Pareto Fronts for Unconstrained Multi-Objective Optimization Problems

Victor Pereyra
pereyra@wai.com

Abstract: Multi-objective optimization is becoming a common tool in Engineering and Scientific applications. Most optimization problems in industry are multi-objective, non-linear, constrained and multi-modal, i.e., very tough. Evolutionary and genetic algorithms are one class of powerful methods that has been favoured in recent times for their robustness, specially in the versions that permit to calculate a discrete representation of the Pareto manifold and the Pareto front. The negative side to these methods is the number of function evaluations required to obtain a reasonable accuracy, which grows exponentially with the dimension of the design parameter space. This is totally inadequate for realistic high fidelity design applications, where function evaluations can be very costly. They still can be useful if one replaces these expensive evaluations by surrogates, as we explain later.

In this paper we show that the Pareto manifold for a convex bi-objective problem can be approximated by solving numerically a two-point boundary value problem and from this insight we mimic technics for the solution of such problems to obtain a continuation method that updates a whole discrete representation of the Pareto manifold while maintaining and even spacing between solutions. As an additional bonus this procedure is easily parallelizable.


FGMRES Preconditioning by Symmetric-Antisymmetric Decomposition of Generalized Stokes Problems

Dany De Cecchis
dcecchis@uc.edu.ve


Hilda López
hlopez@kuaimare.ciens.ucv.ve


Brígida Molina

bmolina@kuaimare.ciens.ucv.ve

Facultad Experimental de Ciencias y Tecnología,
Departamento de Matemática.
Valencia, Venezuela

Abstract: We study the dynamic of two immiscible fluids in a horizontal pipe. The fluids are considered to have similar densities but considerably different viscosities, which is a frequent situation in the transportation of heavy crude oil. The method to solve the variational form of the generalized Stokes problem involves the mixed finite element discretization of the equations, in order to obtain a linear system with a coefficient matrix, symmetric, indefinite, sparse, with a block structure, known as a saddle point matrix. We solve this linear system using a symmetric-antisymmetric decomposition preconditioning technique on the FGMRES method. Comparing with other methods, such as GMRES and MINRES, results show a substantial reduction in the number of iterations and computational time, even for large scale problems.


Finite Element and Finite Difference for the Solution of Reacting Navier-Stokes Equations

Pedro Henrique de Almeida Konzen
phak@mat.ufrgs.br

Álvaro Luiz de Bortoli
dbortoli@mat.ufrgs.br

Mark Thompson
thompson@mat.ufrgs.br

UFRGS - Graduate Program in Applied Mathematics
PPGMAp, Brazil

Abstract: The aim of this work is the solution of a set of reacting Navier-Stokes equations by both the Finite Element and the Finite Difference Methods. The model describes the molecular mixture and the diffusion-reaction of two chemical species to yield a product. The chemical process is approximated by a single-step, irreversible, exothermic Arrhenius type reaction scheme in an incompressible fluid. The time integration follows the explicit Runge-Kutta three-stage scheme for second order time approximation. We also show a local error estimate for the approximation of the exact solution of the problem using the Finite Element Method. The numerical and analytical results contribute to a better understanding of the laminar mixing and reacting process inside a square box.


Fuzzy Ant Colony Optimization for Estimating the Chlorophyll Concentration Profile in Offshore Sea Water

Haroldo Fraga de Campos Velho
haroldo@lac.inpe.br

Adenilson Carvalho
adenilson@lac.inpe.br

Roberto P. Souto

José C. Becceneri
becce@lac.inpe.br

Sandra A. Sandri

Stephan Stephany

LAC-INPE
Sao Jose dos Campos, Sao Paulo, Brazil

Abstract: Optical properties in the offshore sea water can be described by means of bio-optical models, where the vertical profiles of the absorption and scattering coefficients are related with the chlorophyll profile [2]. Therefore, the determination of some inherent optical properties can be addressed by estimating the ocean chlorophyll concentration. This inverse problem can be formulated as an optimization problem and iteratively solved, where the radiative transfer equation is the direct model. An objective function is given by the square difference between computed and experimental radiances at every iteration. Recently, we have used an Ant Colony System (ACS) as the optimizer, where a pre-selection scheme of the candidate solutions is performed by their smoothness, quantified by a Tikhonov norm [1,3]. In the standard ACS method, the pheromone is only reinforced on the best ant of the population (the lowest objective function value) at each iteration. The fuzzy strategy consists to put additional pheromone quantity on the best ant, but a small pheromone quantity is also spread on the other solutions close to the best one, decreasing the pheromone quantity as far as the solution is from the best ant. Each candidate solution corresponds to a discrete Chlorophyll profile. The radiative transfer equation is solved using the Laplace transform discrete ordinate (LTSN) method. Test results show that the fuzzy-ACS produces better inverse solutions.

References
[1] N.N. Arai, R.P. Souto, J.C. Becceneri, S. Stephnay, A.J. Preto, H.F. de Campos Velho (2004): "A new regularization technique for an ant-colony based inverse solver applied to a crystal growth problem",
13th Inverse Problem in Engineering Seminar, (IPES-2004), 14-15 June, University of Cincinnati, Ohio, USA, pp. 147-153.
[2] C.D. Mobley (1994): "Light and Water: Radiative Transfer in Natural Waters", Academic Press.
[3] R.P. Souto, H.F. de Campos Velho, S. Stephany, S. Sandri (2004): "Reconstruction of Chlorophyll Concentration Profile in Offshore Ocean Water using a Parallel Ant Colony Code", 16th European Conference on Artificial Intelligence (ECAI-2004), Hybrid Metaheuristics (HM-2004), 22-24 August, Valencia, Spain, pp. 19-24.


Heisenberg's Turbulent Spectral Transfer Theory for Sub-grid Parameterization in LES Models

Haroldo Fraga de Campos Velho
haroldo@lac.inpe.br

Gervásio A. Degrazia

André B. Nunes

Prakki Satyamurty
saty@cptec.inpe.br

Otávio C. Acevedo

Umberto Rizza

Jonas C. Carvalho
jonas@ulbra.tche.br

LAC-INPE
Sao Jose dos Campos, Sao Paolo
Brazil

Abstract: A turbulent subfilter viscosity for large eddy simulation (LES) models is proposed, based on Heisenberg´s mechanism of energy transfer. Such viscosity is described in terms of a cutoff wavenumber, leading to relationships for the grid mesh spacing in a convective boundary layer. The limiting wavenumber represents a sharp filter separating large and small scales of a turbulent flow and, henceforth, Heisenberg´s model agrees with the physical foundation of LES models. The comparison between Heisenberg´s turbulent viscosity and the classical ones, based on Smagorinsky´s parameterization, shows that both procedures lead to similar subgrid exchange coefficients. With this result, the turbulence resolution length scale and the vertical mesh spacing are expressed only in terms of the longitudinal mesh spacing. Through the employment of spectral observational data in the convective boundary layer, the mesh spacings, the filter width and the subfilter eddy viscosity are described in terms of the convective boundary layer height. The present development shows that Heisenberg´s theory naturally establishes a physical criterium that connects the subgrid terms to the large-scale dimensions of the system.


High Order Adaptive Finite Difference Schemes for Maxwell's Equations

Sônia M. Gomes
soniag@ime.unicamp.br

Margarete O. Domingues
margarete@lac.inpe.br

Paulo J. S. Ferreira
pjf@ieeta.pt

Anamaria Gomide
anamaria@ic.unicamp.br

José R. Ferreira
jrp@det.ua.pt

Pedro Pinho
ppinho@deetc.isel.ipl.pt

IMECC-Unicamp
Campinas SP Brasil

Abstract: In this paper our purpose is to discuss the use of the SPR (Sparse Point Representation) methodology for adaptive finite differences simulations in computational electromagnetics. The principle of the SPR method is to represent the solution only through those point values corresponding to significant wavelet coefficients, which are used as local regularity indicators. Typically, few points are found in each time step, the grids being coarse in smooth regions, and refined close to irregularities. The method has two basic parts: one for function representation and another for the discretization of differential operators. In the representation part, there are wavelet tools containing decomposition and reconstruction operators defined by means of interpolating subdivision schemes. In the other part, spatial derivatives in Maxwell's equations are discretized by traditional uniform finite differences, using step sizes that can be made proportional to each point local scale. We investigate two node arrangements and their effects on the accuracy and stability of high order finite difference schemes. In one case, we consider staggered grids in time-space domain for the magnetic and electric fields, as in the FDTD (Finite Difference Time Domain) scheme. Moreover, we shall also consider the case where the grids coincide for both fields. A theoretical analysis shows that schemes in staggered grids may be preferable from the dispersion view point, especially for low order schemes and coarse grids. However, when adapting the grid density and increasing the order, schemes for non-staggered grids also show good performance. Furthermore, the use of non-staggered grids increases the stability range and it has an easier implementation of adaptive strategies. In this direction, we show numerical simulation results to demonstrate that the SPR method in non-staggered grids has a good potential for computational electromagnetics.


Inferring the Left Ventricle Dynamical Behavior Using a Free-Form Deformations Model

Antonio Bravo
abravo@unet.edu.ve

Rubén Medina
rmedina@ula.ve

Gianfranco Passariello
gpass@usb.ve

Grupo de Bioingeniería
Universidad Nacional Experimental del Táchira
Decanato de Investigación
Venezuela

Abstract: A computational 4-D (3-D + time) model for simulating the dynamical shape of the Left Ventricle (LV) based on Free-Form Deformations (FFD) techniques is described. The simulation model is useful as a teaching tool for understanding the normal or abnormal left ventricle motion. The model is also useful for initializing 3-D segmentation algorithms and for understanding the relation between pathologies and variation of parameters defining the ventricular function. Our model is built from a 3-D surface representation of the LV extracted in a preprocessing stage, for only one time instant of the 4-D image sequence acquired, from a given imaging modality. A segmentation algorithm based on a 2-D Active Appearance Model (AAM) has been used for extracting the endocardial and epicardial walls in a 3-D Multislice Computerized Tomography (MSCT) database of a healthy human. The 3-D surface representation of the LV boundary is inferred using the Delaunay triangulation algorithm based on the 3-D contour points. The simulation process incorporates 7 parameters for describing the left ventricle motion. These parameters are extracted from works previously reported in the literature. Among the possible types of deformation, our model considers longitudinal shortening, radial contraction, circumferential shortening and torsion. The algorithm is implanted using a hierarchical deformation approach, where global deformations are applied first, followed by local deformations. Validation of this computational model is performed by synthesizing 4-D (3-D +time) sequences of the left ventricle, comprising the interval going from end-systole to end-diastole. From the resulting 4D shapes, several mechanical parameters like left ventricle volume, radial contraction and torsion are calculated and compared with results of works previously reported based in MR-tagging images. Comparison is also performed with mechanical parameters extracted from the complementary time instants in the same MSCT database used for extracting the LV wall surfaces required for initialization. First results show a good match between parameters compared.


Mimetic Discretization of Elliptic PDE Problems With Full Tensor Coefficients

Huy K. Vu
huykhanhvu@yahoo.com

Jose E. Castillo
castillo@myth.sdsu.edu

Abstract: This work concentrates on the Mimetic discretization of elliptic partial differential equations (PDE), derived from the application of Darcy's law to flows in Reservoir Simulation. Numerical solutions are obtained and discussed for one-dimensional equations on uniform and irregular grids and two dimensional equations on uniform grids. The focal point is to develop a scheme incorporated with the full tensor coefficients on uniform grids in 2-D. The results of the numerical examples are then compared to previous well-established methods. Based on its conservative properties and global second order of accuracy, this Mimetic scheme shows higher precision in the tests given, especially on the boundaries.


Multiresolution Based Grid Coarsening for Discontinuous Problems

Alfonso Limon
alfonso.limon@cgu.edu

Hedley Morris
edleymorris@yahoo.com

School of Mathematical Sciences,
Claremont Graduate University
Claremont, California, USA

Abstract: Classical multiresolution techniques have been used to simplify the computation of PDEs by concentrating computational resources, in the form of grid refinement, in places where the solution varies sharply. However, classical techniques are affected near solution discontinuities, as Gibb's effects contaminate the wavelet coefficients used to refine the solution. Non-linear adaptive stencil methods, such as the ENO scheme, can reconstruct the solution accurately across jumps, but possess neither the compression capabilities nor the well-understood stability properties of wavelets. Expanding on Ami Harten's ideas, we construct an alternative to wavelet based grid refinement, a multiresolution coarsening method that does not suffer from Gibb's effects and has good compression properties. We will present this alternative grid coarsening method and compare its performance to other multiresolution methods by means of several examples.


Multiscale Analysis by Discrete Mollification

Carlos D. Acosta
cdacosta628@yahoo.es

Cesar G. Castellanos
Email2: gcastell@telesat.com.co

Juan D. Pulgarin
jdpulgaring@unal.edu.co

Abstract: A procedure for multiscale analysis by discrete mollification is introduced. Discrete mollification is a regularization method already implemented in the solution of several ill-posed problems. The multiscale scheme is based on numerical linear algebra results combined with the mollification method applied to the Mallat algorithm. The new technique has a simpler theory, an efficient implementation and compares fairly well with classical wavelet transform procedures. Applications to filtering and reconstruction of 1D signals and images are included.


Nonstandard Methods for More General Reaction Terms

Benito Chen
bchen@uwyo.edu

Hristo Kojouharov
hristo@uta.edu

Department of Mathematics
University of Wyoming
Laramie, Wyoming, USA

Abstract: Nonstandard methods provide exact solutions to differential equations with many different right-hand sides. But there are many others for which the nonstandard exact method cannot be derived. Here we extend the results of a previous paper and obtain a nonstandard method for other right-hand side terms that, though not exact anymore, still have good numerical properties.


Numerical Modeling of Hydrodynamic Processes Forced by Wind and Tide in the Paracas Bay Pisco-Perú

Jorge Quispe Sanchez
jquispe@imarpe.gob.pe

Emanuel Guzman Zorrilla
ejguzman@universia.edu.pe

Instituto del Mar del Perú
Callao, Perú

Abstract: The aim of this study is the investigation of the hydrodynamic of the physical processes in Paracas Bay located in the province of Pisco, Perú. The model employed was the Princeton Ocean Model (POM), which was developed by George Mellor and Allan Blumberg at the Geophysical Fluid Dynamics Laboratory (GFDL).
POM is a sigma coordinate model and solves the basic equations of fluid mechanics using an "Arakawa C" difference scheme for the horizontal grid. To establish the initial and boundary conditions hydrographic, oceanic and meteorological data was acquired, and incorporated into the model to perform the simulations.
The hydrodynamics simulations were performed for 30 days using a Cartesian rectangular grid dx = dy = 390 m and time step dt = 40s. The model was forced with times series of tide (with harmonics constituent) and wind (velocity and direction). The simulation scenes include the three-dimensional barotropic answer, rotational effects, and the results show the fields of currents (velocity and direction) in the bay. Three-dimensional numerical simulations were used to investigate the behavior of currents dynamics and temperature by environmental forcing. Simulations are presented and compared with field data observed. The results contribute to a better understanding of currents velocities and temperature variability in the Paracas Bay.

Key words: Paracas Bay, numerical model, hydrodynamics


Numerical Simulation of a Degenerate PDE Model for the Formation of TCE Degrading Dual-Species Biofilms

HJ Eberl
heberl@uoguelph.ca

Nasim Muhammad

Department of Mathematics and Statistics
University of Guelph
Guelph, ON, Canada

Abstract: Most bacteria live in so-called microbial biofilms. These are microbial communities in which the microrogansims are embedded in a slimy layer of self-produced extracellular polymeric substances (EPS). The EPS gives them protection against harmful environmental impacts such as wash-out or biocides.
While biofilms are considered bad in medical or many industrial applications (infections, biocorrosion), they are beneficially used in environmental engineering applications. In fact, the sorption properties of biofilms are the most efficient contributor to self-purification of surface or sub-surface water.
This is used in biobarrier systems for groundwater protection, where the bacteria remove pollutants such as TCE from the soil. In this presentation we formulate a mathematical model that describes the spatio-temporal development of such a mixed culture biofilm system in a soil pore. It is a coupled system of two doubly-degenerate diffusion-reaction equations for biomass fractions and two semi-linear diffusion-reaction equations for the dissolved substrates. We also present a linearly-implicit numerical scheme for its numerical solution and apply it in a numerical simulatione experiment to study parameter dependencies.


Numerical Solution of Test Neutral Functional Differential Equations with the Segmented Formulation of the Tau Method

René Escalante
rene@cesma.usb.ve

Luis F. Cordero
lfcordero@hotmail.com

Universidad Simón Bolívar
División de Ciencias Físicas y Matemáticas
Departamento de Cómputo Científico y Estadística
Venezuela

Abstract. We use the step by step Tau method to find polynomial approximations to the solution of the nonlinear non-autonomous neutral delay differential equation,

This equation represents, for different values of a, b, c and ?, a family of functional differential equations. It is a generalization of the well-known logistic equation that has been used as a model in population dynamics for single species population growth. Simplified versions of this problem have recently been studied (see [1] and [2]). The Tau method introduced by Lanczos [3] is an important example of how to get approximations of functions defined by a differential equation. In the formulation of a step by step Tau version is expected that the error is minimized at the matching points of successive steps. Through the study of some recent papers ([2], [4], [5]) it seems to be demonstrated that the segmented Tau approximation is a natural and promising strategy in the numerical solution of functional differential equations. Preliminary numerical experiments are consistent with the theorical results reported elsewhere.

Keywords: Nonlinear nonautonomous neutral delay differential equation, Step by step Tau method, Segmented approximation, Population dynamics, Legendre polynomials, Canonical polynomials.

References
[1] Y. Kuang and A. Feldstein, Boundedness of Solutions of a Nonlinear Nonautonomous Neutral Delay Equation, J. Math. Anal. Appl. 156:293-304 (1991).
[2] H.G. Khajah, Tau Method Treatment of a Delayed Negative Feedback Equation, Comput. Math. Appl. 49:1767-1772 (2005).
[3] C. Lanczos, Trigonometric interpolation of empirical and analytical functions, J. Math. Phys. 17:123-199 (1938).
[4] H.G. Khajah and E.L. Ortiz, On a differential-delay equation arising in number theory, Appl. Numer. Math. 21:431-437 (1996).
[5] L.F. Cordero and R. Escalante, Segmented Tau approximation for test neutral functional differential equations. (To appear elsewhere.)


Numerical Treatment of an Inverse Problem for a Strongly Degenerate Parabolic Equation

Anibal Coronel
acoronel@roble.fdo-may.ubiobio.cl

Raimund Burger
rburger@ing-mat.udec.cl

Mauricio Sepulveda
mauricio@ing-mat.udec.cl

Universidad del Bío-Bío, Facultad de Ciencias
Departamento de Ciencias Básicas, Chillán CHILE

Abstract: In this paper we present a numerical method for the identification of parameters in the flux and diffusion functions of a nonlinear strongly degenerate parabolic equation when the solution at fixed time is known. We formulate the identification problem as a minimization of a suitable cost function and derive its formal gradient by means of a first-order perturbation of the state equations, which is a linear strongly degenerate parabolic equation with source term and discontinuous coefficients. For the numerical approach, we discretize the direct problem by the Engquist-Osher scheme and obtain a discrete first-order perturbation associated to this scheme. The conjugate gradient method permits to find numerically the physical parameters.


On a Method for Constructing the Shallow-Water Discrete Models Conserving the Total Mass and Energy

Yuri N. Skiba
skiba@servidor.unam.mx

Denis M. Filatov
pennylane@mail.ru

Centro de Ciencias de la Atmósfera
Universidad Nacional Autónoma de México
México, D.F.

Abstract: In this work, a new method is given for constructing fully discrete shallow-water models (SWMs) which exactly conserve the mass and total energy. The discretization in time is based on using the weak approximation and Crank-Nicolson scheme. The splitting of the SWM operator in geometric coordinates and physical processes provides substantial benefits in the computational cost of the algorithm, as well as in its applicability to a doubly periodic domain on the plane, in a periodic channel on a rotating sphere, and on the whole sphere. Each split fully discrete system conserves the mass and total energy, too. In fact, it suggested a family of finite-difference schemes of different approximation order, either linear or nonlinear, depending on the choice of certain parameters. The method possesses the following important advantages:

1) Unlike all the existing schemes conserving the mass, energy and/or potential entrophy only in the semi-discrete form (discrete in space, but continuous in time), it permits to construct fully discrete mass and total energy conservative shallow-water schemes;
2) In the case of linear schemes, its numerical realization is very cheap, since on each fractional time step, their matrices are M-diagonal and can rapidly be solved by employing fast direct linear solvers. For instance, in the case of a first-order approximation scheme, matrices of the split systems are tridiagonal, and exact solution is rapidly obtained by factorization;
3) Apart from applying on the whole sphere and in the doubly periodic domain on a plane, the method can be utilized for simulating shallow-water flows in a periodic channel with non-periodical lateral boundary conditions.

Results of numerical experiments are discussed. In particular, it is shown that although the discrete models conserve the entrophy only approximately, its oscillations are rather small.

References
1. T.D. Ringler & D.A. Randall, A Potential Enstrophy and Energy Conserving Numerical Scheme for Solution of the Shallow-Water Equations on a Geodesic Grid, Mon. Wea. Rev., 130 (2002) 1397-1410.
2. R. Salmon, Poisson-Bracket Approach to the Construction of Energy- and Potential-Enstrophy-Conserving Algorithms for the Shallow-Water Equations, J. Atmosph. Sci., 61 (2004) 2016-2036.
3. Yu.N. Skiba, Finite-Difference Mass and Total Energy Conserving Schemes for Shallow-Water Equations, Meteor. & Hydrol., 2 (1995) 55-65.
4. Skiba Yu.N. & D. Filatov, Esquemas Conservativos, Basados en el Método de Separación, para la Simulación Numérica de Vórtices en la Atmósfera. Interciencia, 3 (1) (2006) 16-21.


On Generation of Conformal Mappings of Spherical Domains

Andrei Bourchtein
email: burstein@terra.com.br

Ludmila Bourchtein
bourchtein@terra.com.br

Abstract: The problem of planar representation of a part of sphere surface is one of the principal and oldest problems of cartography. In the last decades, such representations have been used in geophysical computational fluid dynamics for determining the properties of computational grids. In this study, we consider the problem of the construction of the planar projections with given properties in the class of conformal mappings. The problem of restoring the conformal mappings starting from a given scale function is solved for arbitrary spherical domain in the class of the projections with mapping factor depending only on the latitude. The problem of the minimum distortion mapping is solved for a spherical disc in the class of all conformal mappings. The results obtained are compared with traditional mappings from a sphere onto a plane.


On the Parameter Selection Problem in the Newton-ADI Iteration for Large Scale Riccati Equations

Hermann Mena
hmena@server.epn.edu.ec

Peter Benner
benner@mathematik.tu-chemnitz.de

Jens Saak
jens.saak@mathematik.tu-chemnitz.de

Abstract: The numerical treatment of linear-quadratic regulator problems for parabolic partial differential equations (PDEs) requires the solution of large scale Riccati equations. The Newton-ADI iteration is an efficient numerical method for this task. It requires the solution of a Lyapunov equation by the alternating directions implicit (ADI) algorithm in each iteration step. Here, we study the selection of shift parameters for this iteration. This leads to a rational minimax problem which has been considered by many authors. Since knowledge about the complete complex spectrum is crucial for computing the optimal solution this is infeasible for the large scale systems arising from finite element discretization of PDEs. Therefore several alternatives for computing suboptimal parameters are discussed and compared in numerical examples.


Optimal Power Split in a Hybrid Electric Vehicle Using Direct Transcription of an Optimal Control Problem

Elvio A. Pilotta
pilotta@mate.uncor.edu

Laura V. Pérez
lperez@ing.unrc.edu.ar

Universidad Nacional de Córdoba
Ciudad Universitaria, Argentina

Abstract: To efficiently operate electromechanical systems powered by two energy sources, it is necessary to determine the instantaneous power split between sources in order to minimize the energy consumption of the whole system. In this work, this problem is posed as a nonlinear finite horizon optimal control problem with control and state constraints and solved using a direct transcription approach. This means that the problem is fully discretized in time and the resulting finite dimensional optimization problem is solved using a nonlinear programming (NLP) code. This work describes the application to the case of the hybrid electric vehicle (HEV) that is being developed in the Applied Electronics Group (GEA) at the University of Rio Cuarto (Cordoba). The statement and discretization of the control problem as well as the setting for using the NLP code (MINOS) are described. Numerical experiments and comparisons with those obtained by different approaches are presented.


Optimization of Solar Low Energy Building Design

María Isabel Pontin
mpontin@ing.unrc.edu.ar

María Nidia Ziletti
mziletti@ing.unrc.edu.ar

Alejandra Mendez
amendez@ing.unrc.edu.ar

Abstract: This paper presents a simple quantitative procedure for the optimum bioclimatic building design. An efficient building design will be performed using strategies like passive solar heating, passive cooling and natural ventilation, and daylighting. Solar radiation is the most important contribution to the energy balance during the daytime. Utilization of daylight in buildings may result in significant savings in electricity consumption for lighting while creating a higher quality indoor environment. Additional energy savings may also be realized during cooling season, when reduction of internal heat gains due to electric lighting results in a corresponding reduction of cooling energy consumption. The present work includes the application of heuristic techniques in order to find the optimum building design in terms of energy and cost. A case study that shows the applicability of this approach is presented. The resulting design is compared with the existing design and some alternatives for improving the realized building are presented. Keywords: Solar design, Bioclimatic design, Optimization, Energy conservation.


Orthogonal Polytopes Modeling Through the Extreme Vertices Model in the n-Dimensional Space

Ricardo Pérez-Aguila
104378@prodigy.net.mx

Antonio Aguilera

Universidad de las Américas
Puebla, México

Abstract: The Extreme Vertices Model (EVM-3D) was originally presented, and widely described, by Aguilera & Ayala for representing 2-manifold Orthogonal Polyhedra (1997) and later considering both Orthogonal Polyhedra (3D-OPs) and Pseudo-Polyhedra (3D-OPPs, 1998). This model has enabled the development of simple and robust algorithms for performing the most usual and demanding tasks on solid modeling, such as closed and regularized Boolean operations, solid splitting, set membership classification operations and measure operations on 3D-OPPs. It is natural to ask if the EVM can be extended for modeling n-Dimensional Orthogonal Pseudo-Polytopes (nD-OPPs). In this sense, some experiments have been made, by Pérez-Aguila & Aguilera (2003), where the validity of the model was assumed true in order to represent 4D and 5D-OPPs. The results obtained have leaded us to state, and to prove in a formal way, that the Extreme Vertices Model in the n-Dimensional Space (EVM-nD) is a complete scheme for the representation of nD-OPPs. The meaning of complete scheme is based in Requicha's set of formal criterions that every scheme must have rigorously defined: Domain, Completeness, Uniqueness and Validity (1980).

The purpose of this presentation is to show the way the Extreme Vertices Model allows representing nD-OPPs by means of a single subset of their vertices: the Extreme Vertices. It will be seen how the Odd Edge Combinatorial Topological Characterization in the nD-OPPs has a paramount role in the foundations of the EVM-nD. Although the EVM of an nD-OPP has been defined as a subset of the nD-OPP's vertices, there is much more information about the polytope hidden within this subset of vertices. We will show the procedures and algorithms in order to obtain this information.


Out-of-Core layer of UCSparseLib

German Larrazabal
glarraza@uc.edu.ve

Jorge Castellanos
jcastelld@uc.edu.ve

Multidisciplinary Center of Scientific Visualization and Computing (CEMVICC)
Valencia, Estado Carabobo, Venezuela

Abstract: In this work, we present the out-of-core layer of UCSparseLib. UCSparseLib is a numerical library to solve dense and sparse linear systems. This library is used in several applications, such as, a black oil simulator, seismic simulator, an ocean simulator, etc. The out-of-core layer permits to handle large matrices (dense or sparse). The out-of-core layer is a black box for the users. We show the performance of UCSparseLib when its out-of-core layer is on.


Parameter Identification of Nonlinear Dynamical Models by Using Differential Evolution Algorithms

Irineo Lopez-Cruz
ilopez@correo.chapingo.mx

Noel Lopez-Gonzaga
40501423@escolar.unam.mx

Universidad Autonoma Chapingo
Texcoco, Edo. de Mexico

Abstract: Both crops growth and greenhouse climate models are highly nonlinear and also they have many parameters that may affect quality of model's predictions. In order to use dynamical models for optimization and control purposes it is required to estimate accurately their most sensitive parameters. Mathematically, parameter identification can be address by solving an optimization problem. Although, local search methods, such as nonlinear least squares, can be applied to solve the parameter optimization problem, because of nonlinearities and correlation among parameters, a non-convex problem and multiple local minima are likely. Hence, the use of global optimization such as evolutionary algorithms would be preferable. Differential Evolution Algorithms (DEAs) are very efficient in solving parameter optimization problems. Therefore, in this research DEAs were applied to minimize the norm of a vector containing modeling's errors. A physical nonlinear model of air temperature and humidity of a Mexican greenhouse and also a nonlinear and high-dimensional crops growth and development generic model (SUCROS a Simple and Universal CROp growth Simulator), were used to test the performance of DEAs. Both dynamical models and also DE algorithms were programmed using the Matlab-Simulink environment. Dynamical models predictions were compared with actual measurements of state and output variables. Results showed that DEAs improve the predictions of the models and therefore they are able to solve the identification problem adequately.


Preconditioning Techniques for Saddle Points Problems

Zenaida Castillo
zenaida@kuaimare.ciens.ucv.ve

Universidad Central de Venezuela
Facultad de Ciencias
Escuela de Computacion
Centro de Calculo Cientifico y Tecnologico
Los Chaguaramos, Caracas, Venezuela

Abstract: We present a Sparse Approximate Inverse Preconditioner (SPAI) for solving linear systems resulting in saddle point problems. These problems arise frequently in fluid dynamics, after the discretization of the Navier Stokes equations. We developed this preconditioner based on the sparsity pattern of the coefficient matrix for saddle point problems. The computation of the preconditioner involves solving a set of uncoupled least squares problems, which can be parallelized easily on distributed memory machines. The performance and scalability of parallel GMRES and CG methods with this inverse preconditioner is tested on several problems. The results show that the inverse preconditioner performs well in the test cases and can be the method of choice for solving large-scale problems.


Sphere Inversion and 3D Lemniscates Singularities

Gabriel Arcos
gabrielarcos@gmail.com

Marco Paluszny
marco@euler.ciens.ucv.ve

José R. Ortega
jortega@uc.edu.ve

Abstract: Given a finite set of fixed points, we define the distance polynomial function as the product of square distances to the given points. A level set of this function is called a 3D lemniscate. We present a new interpretation of 3D lemniscates singularities. Given a unit sphere centered at a point other than the foci, if the barycenter of the foci's inverses, with respect to that sphere, coincides with the center, then it is a singularity of the distance polynomial function. This gives us a geometric approach to develop tools to deform 3D lemniscates in a predictable fashion by keeping invariant the barycentric property.


The Method of Meshless Fundamental Solutions for the Pressure Equation in Oil Field Problems

Desireé Villalta
desi090680@yahoo.com

Juan Guevara-Jordan
jguevara@euler.ciens.ucv.ve

Mariela Castillo

mcastill@euler.ciens.ucv.ve

Departamento de Cómputo Científico y Estadística
Universidad Simón Bolívar.
Sartenejas, Baruta, Edo. Miranda, Caracas, Venezuela


Abstract: A new mesh free numerical method for solving the unsteady state pressure equation in oil field problems is presented. It is well known that standard numerical methods are not well adapted to approximate the pressure in this context. The new method combines the fundamental solution and singular value decomposition methods to obtain a very simple and robust numerical algorithm for modeling pressure evolution in a reservoir. The theoretical description of the new method and numerical results from its implementation will be offered. The numerical results show excellent agreement with analytic solutions in validation problems. A comparative study of the new method against standard finite element method in an arbitrary shaped reservoir with multiple wells will be analyzed. It gives evidence that the proposed method has considerable advantages over traditional finite and boundary elements approaches.


The Simulation of The Circulation in Todos Santos Bay, Mexico

Isabel Ramirez
iramirez@cicese.mx

Carlos Torres
ctorres@uabc.mx


Adan Mejia
amejia@uabc.mx

Abstract: Todos Santos Bay is located at the Pacific Coast of Mexico, one hundred miles from the border with US. It has 15 kilometers in the main axes and it an average depth of 30 meters. A canyon of 600 meters deep and an island in the front of the bay create a complex pattern of circulation. The effect of the tide driving the circulation is clearly showed with measurements. Meanwhile the effect of the wind is show in the depth variability of the current velocity. The meassured scenario is reproduced using a tridimentional model derived from TRIM.


Transformation Algorithm of a Matrix that Determines the Stability in Square Mean of a Dynamical Input-Output System

José Ramón Guzmán
jrg@servidor.unam.mx

Alejandra Calvo Flores
ale_cf@hotmail.com

Gabriela Marmolejo Franco
hola_gmf@hotmail.com

Instituto de Investigaciones Económicas
Universidad Nacional Autónoma de México
México, D.F., México

Abstract: When considering stochastic perturbations of a dynamical input-output system of amounts-prices there is a dynamical system associated that determines the square mean dynamics. Of this last system a d²×d² matrix for the investigation of the mean square stability is obtained. Here is proposed a general algorithm that transforms the original matrix to one of order (d(d+1)/2)×(d(d+1)/2), conserving the same information of the eigenvalues. This algorithm is useful in the reduction of the time needed for the eigenvalues calculations.


Two New Algorithms for the Joint Replenishment Problem

Miguel Angel Gutierrez
gamma@xanum.uam.mx

John Goddard
jgc@xanum.uam.mx

Sergio de los Cobos Silva
cobos@xanum.uam.mx

Departamento de Ingeniería Eléctrica
Universidad Autónoma Metropolitana-Iztapalapa
México, D.F.

Abstract: In this work a multi-product inventory problem, known in the literature as the Joint Replenishment Problem (JRP), is solved. The JRP has a continuous decision variable and as many discrete decision variables as the number of items that are ordered and produced. An exact method for this problem exists, given by Goyal, which for a large number of discrete decision variables becomes computationally prohibitive. Several heuristic algorithms have also been introduced to solve the JRP, the best such algorithm reported so far is called RAND. Here two new algorithms are proposed that are based on the continuous part of the problem: the first employs scattered search, and the other partitions the range of the continuous variable in m equal parts and a solution is sought in each subinterval, using golden section search. Both algorithms were compared with RAND on randomly generated examples. It was found that the first algorithm, using scattered search, correctly located the optimal solution for each of the examples. For the second algorithm, using golden section, it was found that in all cases an equal or better result to RAND was obtained.


Water Uptake by Root of Croops: A Moving Boundary Approach

Jorge Luis Blengino Albrieu
jblengino@exa.unrc.edu.ar

Juan Carlos Reginato
jreginato@exa.unrc.edu.ar

Domingo A. Tarzia
Domingo.Tarzia@fce.austral.edu.ar

UNRC, Córdoba, Argentina

Abstract: The available models of water uptake by roots of crops do not take into account the root growth, since they solve the governing equations on a fixed domain (Molz 1981). Recently it has been reported a model that takes into account the simultaneous connection between nutrients uptake and root growth (Reginato et al., 2000) by means of the formulation of a moving boundary problem that solves the system of equations for a moving domain (the growing root system). A moving boundary model for water uptake is formulated for the process of water uptake taking into account the plant as an organism in constant growth. In this communication we will report some theoretical results with respect to the water uptake model for plants growing mainly in clay soils. The plants grows in a fixed volume of soil (as in flowerpots). The model is solved by means of the application of the method of dominion immobilization and later application of the finite element method. Under these conditions diagrams of sensitivity for soil and plant parameters are obtained.