2021/12/01 by Sasan Mohyaddin, Mohyaddin, Sasan, Johannes Tausch +1
Engineering · Physics and Astronomy · #65N12 #65N30 #65N38 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #G.1.8 #G.1.9 #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2112.00864
openalex publication_date 2021/12/01 · openalex created_date 2022/11/09 · openalex updated_date 2026/07/28
Three algorithm are proposed to evaluate volume potentials that arise in\nboundary element methods for elliptic PDEs. The approach is to apply a modified\nfast multipole method for a boundary concentrated volume mesh. If h is the\nmeshwidth of the boundary, then the volume is discretized using nearly\nO(h-2) degrees of freedom, and the algorithm computes potentials in nearly\nO(h-2) complexity. Here nearly means that logarithmic terms of h may\nappear. Thus the complexity of volume potentials calculations is of the same\nasymptotic order as boundary potentials. For sources and potentials with\nsufficient regularity the parameters of the algorithm can be designed such that\nthe error of the approximated potential converges at any specified rate\nO(hp). The accuracy and effectiveness of the proposed algorithms are\ndemonstrated for potentials of the Poisson equation in three dimensions.\n