Convergence Analysis of the Dirichlet-Neumann Iteration for Finite Element Discretizations

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Abstract

We analyze the convergence rate of the Dirichlet-Neumann iteration for the fully discretized unsteady transmission problem. Specifically, we consider the coupling of two linear heat equations on two identical non overlapping domains with jumps in the material coefficients across these. In this context, we derive the iteration matrix of the coupled problem. In the 1D case, the spectral radius of the iteration matrix tends to the ratio of heat conductivities in the semidiscrete spatial limit, but to the ratio of the products of density and specific heat capacity in the semidiscrete temporal one. This explains the fast convergence previously observed for cases with strong jumps in the material coefficients.

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Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Beräkningsmatematik
Originalspråkengelska
Sidor (från-till)733-734
Antal sidor2
TidskriftPAMM - Proceedings in Applied Mathematics and Mechanics
Volym16
StatusPublished - 2016 okt 25
PublikationskategoriForskning
Peer review utfördJa
EvenemangJoint 87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mathematiker-Vereinigung (DMV), Braunschweig 2016 - Braunschweig, Tyskland
Varaktighet: 2016 mar 72016 mar 11