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

详细信息    查看全文

• 作者：Michael Messner ; Martin Schanz ; Johannes Tausch
• 关键词：Parabolic FMM ; Fast Gauss transform ; Galerkin BEM ; Heat equation
• 刊名：Journal of Computational Physics
• 出版年：1 February, 2014
• 年：2014
• 卷：258
• 期：Complete
• 页码：15-30
• 全文大小：571 K

文摘

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.