A fast Galerkin method for parabolic space-time boundary integral equations

Authors:
Michael Messner;Martin Schanz;Johannes Tausch
Affiliations:
Institute of Applied Mechanics, Graz University of Technology, Technikerstraíe 4/II, 8010 Graz, Austria;Institute of Applied Mechanics, Graz University of Technology, Technikerstraíe 4/II, 8010 Graz, Austria;Mathematics Department, Southern Methodist University, 209B Clements Hall, Dallas, TX 75275-0156, USA
Venue:
Journal of Computational Physics
Year:
2014

Citing 5
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Abstract

An efficient scheme for solving boundary integral equations of the heat equation based on the Galerkin method is introduced. The parabolic fast multipole method (pFMM) is applied to accelerate the evaluation of the thermal layer potentials. In order to remain attractive for a wide range of applications, a key issue is to ensure efficiency for a big variety of temporal to spatial mesh ratios. Within the parabolic Galerkin FMM (pGFMM) it turns out that the temporal nearfield can become very costly. To that end, a modified fast Gauss transform (FGT) is developed. The complexity and convergence behavior of the method are analyzed and numerically investigated on a range of model problems. The results demonstrate that the complexity is nearly optimal in the number of discretization parameters while the convergence rate of the Galerkin method is preserved.