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Efficient simulations of large-scale convective heat transfer problems

Goik Damian, Banaś Krzysztof, Bielański Jan, Chłoń Kazimierz

Computer Science

2021

T. 22 (4)

517--538

We describe an approach for efficient solution of large-scale convective heat transfer problems that are formulated as coupled unsteady heat conduction and incompressible fluid-flow equations. The original problem is discretized over time using classical implicit methods, while stabilized finite elements are used for space discretization. The algorithm employed for the discretization of the fluid-flow problem uses Picard’s iterations to solve the arising nonlinear equations. Both problems (the heat transfer and Navier–Stokes equations) give rise to large sparse systems of linear equations. The systems are solved by using an iterative GMRES solver with suitable preconditioning. For the incompressible flow equations, we employ a special preconditioner that is based on an algebraic multigrid (AMG) technique. This paper presents algorithmic and implementation details of the solution procedure, which is suitably tuned – especially for ill-conditioned systems that arise from discretizations of incompressible Navier–Stokes equations. We describe a parallel implementation of the solver using MPI and elements from the PETSC library. The scalability of the solver is favorably compared with other methods, such as direct solvers and the standard GMRES method with ILU preconditioning.

Parallel methods for matrix computations obtained in FEM

Wencel J., Smykowski J., Katarzyński P., Szymański G.

Przegląd Elektrotechniczny

2007

R. 83, nr 11

32-34

The paper presents methods which could be used to accelerate solving models of electromagnetic devices. The modelling technique is discussed both with the most crucial parts of modelling process. The most cost-effective computational issues are spread to solve them using several parallel solvers. Two libraries for distributed computing were used in calculations to compare their speed and effectiveness.

Niniejsze opracowanie prezentuje metody, które można wykorzystać do przyspieszenia procesu modelowania urządzeń elektromagnetycznych. Zaprezentowana została technika tworzenia modelu i związane z nią najbardziej istotne części procesu modelowania. Zagadnienia obliczeniowe o najwyższych czasowych kosztach realizacji podległy rozproszeniu tak, aby możliwe było zastosowanie równoległych środowisk przetwarzających. Do obliczeń rozproszonych wykorzystano dwie biblioteki, celem porównania ich prędkości działania i wydajności.