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First-Kind Boundary Integral Equations for the Hodge-Helmholtz Equation
(2017)SAM Research ReportReport -
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Second Kind Boundary Integral Equation for Multi-Subdomain Diffusion Problems
(2016)Research ReportReport -
Splitting-Based Structure Preserving Discretizations for Magnetohydrodynamics
(2017)SAM Research ReportReport -
Hyperbolic cross approximation for the spatially homogeneous Boltzmann equation
(2012)Research ReportThe nonlinear spatially homogeneous integro-differential Boltzmann equation is a uniquely challenging task for numerical solvers due to the difficulty of efficiently computing the collision operator. A popular method is to expand the solution in Fourier modes and to truncate the collision operator. We present an approach based on the hyperbolic cross, whereby the performance can be greatly enhanced in some situations, as well as an offset ...Report -
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DG Treatment of Non-Conforming Interfaces in 3D Curl-Curl Problems
(2014)Research ReportWe consider 3D Curl-Curl type of problems in the presence of arbitrary,non-conforming mesh-interfaces. The Interior Penalty/Nitsche’s Method is ex-tended to these problems for edge functions of the first kind. We present an a priori error estimate which indicates that one order of convergence is lost in comparison to conforming meshes due to insufficient approximation properties of edge functions. This estimate is sharp for first order ...Report -