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- Kent-André Mardal, Ola Skavhaug, Glenn Terje Lines, Gunnar Andreas Staff, Åsmund Ødegård
- Computing in Science & Engineering
- 2007

This article describes two Python modules for solving partial differential equations (PDEs): PyCC is designed as a Matlab-like environment for writing algorithms for solving PDEs, and SyFi creates matrices based on symbolic mathematics, code generation, and the finite element method.

- Kent-André Mardal, Trygve K. Nilssen, Gunnar Andreas Staff
- SIAM J. Scientific Computing
- 2007

In this paper we show that standard preconditioners for parabolic PDEs discretized by implicit Euler or Crank–Nicolson schemes can be reused for higher–order fully implicit Runge–Kutta time discretization schemes. We prove that the suggested block diagonal preconditioners are order–optimal for A–stable and irreducible Runge–Kutta schemes with invertible… (More)

Recently, the authors introduced a preconditioner for the linear systems that arise from fully implicit Runge-Kutta time stepping schemes applied to parabolic PDEs [9]. The preconditioner was a block Jacobi preconditioner, where each of the blocks were based on standard preconditioners for low-order time discretizations like implicit Euler or… (More)

Gunnar A. Staff and Kent-Andre Mardal and Trygve K. Nilssen ∗ Simula Research Laboratory 1325 Lysaker, Norway e-mail: gunnaran@simula.no web page:http://www.simula.no/portal memberdata/gunnaran † Simula Research Laboratory 1325 Lysaker, Norway e-mail:kent-and@simula.no web page:http://www.simula.no/portal memberdata/kent-and †† Scandpower Petrolium… (More)

This paper represents one of the contributions at a minisymposium on the Parareal algorithm at this domain decomposition conference. The minisymposium was organized by Professor Yvon Maday, who is also one of the originators of the Parareal algorithm. The main objective is to be able to integrate a set of differential equations using domain decomposition… (More)

- Trygve K. Nilssen, Gunnar Andreas Staff, KENT–ANDRE MARDAL
- 2009

Abstract. The PDE part of the bidomain equations is discretized in time with fully implicit Runge–Kutta methods, and the resulting block systems are preconditioned with a block diagonal preconditioner. By studying the time stepping operator in the proper Sobolev spaces we show that the preconditioned systems have bounded condition numbers given that the… (More)

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