Development of high performance numerical methods for solving stiff multiparameter boundary value problems

Información del proyecto

Identificador del acuerdo de subvención: INTAS-RFBR95-0098

Fecha de inicio

Fecha de finalización

Financiado con arreglo a

• International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993-

Coste total

Sin datos

Aportación de la UE

Sin datos

Coordinado por

Katholieke Universiteit Nijmegen
Netherlands

Objetivo

Stiff multiparameter boundary value problems for elliptic systems of differential equations and development of appropriate numerical methods for them are the topic of our interest. The problems of such a type arise, for example, in theory elasticity. Consideration of composite material problems and their numerical solution leads normally to very large sized and extremely illconditioned algebraic systems of equations, when discretized by finite element, difference or similar methods. When the original equations have one or more highly varying parameters, then the condition number depends on the coefficient jumps and standard solution methods fail to be applicable. Similarly, certain nonlinear problems as arising in non newtonian fluids give rise to large nonlinear and even indefinite systems. The goal of this project is development of effective numerical methods for the solution of these problems which are, in additional, efficient on (massively) parallel computer architecture. There are various approaches taken for these. The first one is construction of the preconditioner matrix in such a way that equivalence constants do not depend on coefficients jumps. The second approach is to reconstruct the original problem to another form of notation using Shur compliment operator. As was shown in recent papers it was managed to solve number of problems with the help of this approach, but all considerations were realized only for the differential case. Thus the problem of construction of appropriate finite element method in such a way that main properties of differential operators were preserved and implementation of obtained technique was possible is urgent. Finally, the third approach is to reduce original elliptic problem to the equation system of first order and to use the finite element-least squares method approximation. It allows to use ordinary finite elements, for which were developed corresponding approximation theory. In this case, it appears the problem of construction of an effective method of algebraic equations system solving and theory extension, which was developed for the case of second order equations. Also there arises the problem of development of the same theory for the case of more general systems of elliptic partial differential equations of the first order. All these open problems will be considered in a joint effort of the research team, whose members have somewhat different research experience, but together as a whole have (more than) a necessary knowledge for these tasks. The results will be presented first at workshops and at seminars during mutual visits to various groups by some of the participating scientists. They will later be presented in research reports to be submitted to international scientific journals in numerical analysis, computer science and engineering.

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Programa(s)

• IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993-

Tema(s)

• 2 - Mathematics, Telecommunications, Information Technologies

Convocatoria de propuestas

Datos no disponibles

Régimen de financiación

Datos no disponibles

Coordinador

Katholieke Universiteit Nijmegen

• Aportación de la UE: Sin datos
• Dirección: 6525 ED Nijmegen ; Países Bajos
• Coste total: Sin datos

Participantes (1)

Moscow State University ' M.V. Lomonosov '

Rusia

• Aportación de la UE: Sin datos
• Dirección: 119899 Moscow
• Coste total: Sin datos