Gunnar Andreas Staff

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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)
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)
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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