Organizers Elvio A. Pilotta pilotta@mate.uncor.edu Adriana B. Verdiell averdiel@criba.edu.ar

Speakers Vera Lucia Rocha Lopes, "Inverse q-Columns ......" vlopes@ime.unicamp.br Graciela Sottosanto, "Auhmented Penalization ......" gsotto@uncoma.edu.ar Adriana B. Verdiell, "A Trust-Region ......" averdiel@criba.edu.ar Elvio A. Pilotta, "A Spectral Projected ......" pilotta@mate.uncor.edu

Abstract: Numerical methods for large-scale nonlinear programming problems are presented in this session. Quasi-Newton methods are suitable to be used when the Hessian is too expensive to compute or it is not available. The methods proposed in this session use firs order information, avoid excessive computational effort and exploit the particular struc ture of the problem formulation. Quasi-Newton methods, trust-region approach, spectral gradient methods are strategies that work very well to treat large-scale optimization problems.

---

Organizers Claudia A. Sagastizábal sagastiz@impa.br

Speakers Edmundo Rofman, "On Traffic Light ......" edmundo.rofman@inria.fr Carlos Martin, "Multiexponetial Fit ......" martin@famaf.uncor.edu José P. Tamagno, "Numerical Simulation ......" jtamagno@com.uncor.edu Claudia A. Sagastizábal, "Optimal Planning ......" sagastiz@impa.br

Abstract: This miniworkshop gathers some important applications of mathematics to both Engineering and Physical Sciences in Latin America. Specifically, we will discuss:
- Optimal planning of the electric power mix in Brazil (with an horizon of 10 or more years)
- Some applications of optimal control and Aerounautical Engineering
- Optimal data fitting in Physics.

---

Organizers María Cristina Sanziel sanziel@fceia.unr.edu.ar "Sufficients Conditions To......"

Speakers Mabel A. Medina, "Phase change in metal ......" mmedina@fceia.unr.edu.ar Pedro Roberto Marangunic, "Non-Essential Blow-up ......" Mariela C. Olguín, "Numerica Simulation of A Stefan ......" mcolguin@fceia.unr.edu.ar Angélica Bouciguez, "The use of phase ......"

Abstract: Phase-change processes are present in different problems of Applied Mathematics. They appear in the siderurgical industry, frigorific industry (food freezing), metallurgy (binary alloy solidification, metal soldering), plastics (solidification of various products), nuclear technology (accident prevention by fusion of radiactiv material), profit of solar energy and in many other applications. For that reason, many mathematicians, physicisys, chemists and engineers are interested in these themes, and there is substantial development. We are going to analyze some problems with phase-change in various applications, from the points of view of theory, numerical analysis and numerical simulations.

---

Organizers Sonia Maria Gomes soniag@ime.unicamp.br

Speakers Margarete Oliveira Domingues, "Adaptive Wavelet ......" margaret@cptec.inpe.br Magda Kimico Kaibara, "A Fully Adaptive ......" kaibara@fc.unesp.br Jorge Lizardo Díaz Calle, "Implicit Discontinuous ......" calle@fec.unicamp.br José Eduardo Castilho, "Stability Analysis ......" jecastilho@ufu.br

Abstract: Motivation: Solutions to many interesting flow problems frequently exhibit singular features, such as sharp transition layers, propagating steep fronts or pronounced spikes, whose reliable numerical approximation present challenging computational tasks. Uniform gridding is not practical, since high resolution is only needed in small regions, where irregularities occur. Therefore, significant improvements in computational efficiency may be obtained by authomatically adapting the grid in which the discretization of the solution is performed. In comput ational fluid dynamics, there are several approaches for the construction of such adapted meshes. Nowadays, a new kind of adaptive criteria is becoming useful. The decision whether the grid is refined or unrefined in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators for local smootheness of the numerical solution. The presentations of the present mini-workshop shall be concerned with such class of methods. The main purpose is to give an overview of recent results obtained by a Brazilian numerical analysis group coordinated by the organizer.

Outline: Numerical examples shall be presented in order to illustrate the performance of adaptive wavelet strategies when combined with traditional schemes. In this direction, the first three presentations shall be concerned with the use of wavelets for adaptive calculations in finite differences, finite volumes, and the discontinuous Galerkin method. One of the main atractive aspects of such adaptive solvers is that they can be separated into two parts: the operator part and the representation part. The operator part is performed by a standard scheme that may be chosen by means of stability and consistency criteria. Therefore, the solver can benefit from the considerable advances achieved in the corresponding area. The representation part is formulated in the context of wavelet data compression. This is a more recent topic, but a rigorous study of the effectiveness of such nonlinear approximation has already been stablished in the wavelet literature. In a multilevel context, it is tempting to consider a higher degree of efficiency by using local time steps that depend on the level of refinement. In wavelet analysis, this was first considered by Bacry, Mallat and Papanicolau (1992). Focusing only on the time adaptation aspect, the study of the last presentation indicates, for a model problem, that the stability and consistency conditions for the reference scheme also hold for the its time-adaptive version.

---