Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: sparse linear equations

Sortuj według:

Ogranicz wyniki do:

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.

Supernodal algorithm versus object oriented technique in sparse linear equations solver

Stabrowski M.

Przegląd Elektrotechniczny

2005

R. 81, nr 2

44-47

Supernodal technique, used in the field of sparse linear equation solvers, introduces dense kernel for speeding-up the computations. SuperLU solver is the most sophisticated and efficient example of this technique. The research reported here shows that supernodal solver is really fast, but this spectacular speed is obtained through abandoning of numerical stability. It has been shown that SuperLU solver fails in whole class of practical real-world problems. An attempt to characterize and diagnose this problems in terms of matrix parameters has been madę. Pointer solver, being stable numerically and fairly fast alternative for supernodal solver is presented quite comprehensively.

Metoda superwęzłów stosowana przy rozwiązywaniu rzadkich układów równań algebraicznych polega na specjalnym traktowaniu przydiagonalnych fragmentów macierzy rzadkich. Fragmenty te traktowane są jako submacierze pełne, przez co uzyskuje się przyspieszenie obliczeń kosztem, jak podają niektórzy badacze, utraty stabilności numerycznej. Praca jest próbą analizy tego problemu w kategoriach parametrów macierzy rozwiązywanego układu równań. Przedstawia stabilną numerycznie i dość szybką alternatywę - solver ,,wskaźnikowy" (pointer solver).