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Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems

Owe Axelsson, János Karátson (2013)

Open Mathematics

A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green’s functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.

High degree precision decomposition method for the evolution problem with an operator under a split form

Zurab Gegechkori, Jemal Rogava, Mikheil Tsiklauri (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In the present work the symmetrized sequential-parallel decomposition method of the third degree precision for the solution of Cauchy abstract problem with an operator under a split form, is presented. The third degree precision is reached by introducing a complex coefficient with the positive real part. For the considered schema the explicit a priori estimation is obtained.

High degree precision decomposition method for the evolution problem with an operator under a split form

Zurab Gegechkori, Jemal Rogava, Mikheil Tsiklauri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In the present work the symmetrized sequential-parallel decomposition method of the third degree precision for the solution of Cauchy abstract problem with an operator under a split form, is presented. The third degree precision is reached by introducing a complex coefficient with the positive real part. For the considered schema the explicit a priori estimation is obtained.

Hybrid parallelization of an adaptive finite element code

Axel Voigt, Thomas Witkowski (2010)

Kybernetika

We present a hybrid OpenMP/MPI parallelization of the finite element method that is suitable to make use of modern high performance computers. These are usually built from a large bulk of multi-core systems connected by a fast network. Our parallelization method is based firstly on domain decomposition to divide the large problem into small chunks. Each of them is then solved on a multi-core system using parallel assembling, solution and error estimation. To make domain decomposition for both, the...

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