Titlebook: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1; Selected Papers from Jens M. Melenk,Ilaria Perugia,Chri

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Broadband Recursive Skeletonizationt of techniques such as the Fast Multipole Method, Fast Direct Solvers, .-matrix methods, etc. These algorithms depend crucially on the low-rank approximation of dense interactions between disjoint subsets of the computational domain. The key result of the present work is the discovery that for time

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A Novel Spectral Method for the Subdiffusion Equationsually singular near the initial time. Consequently, direct application of the traditional high-order numerical methods is inefficient. We try to overcome this difficulty in a novel approach by combining variable transformation techniques with spectral methods. The idea is to first use suitable vari

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Taming the CFL Number for Discontinuous Galerkin Methods by Local Exponentiationhis approach is expensive as the matrix is dense and necessitates global communication. In this paper, we propose a local low-rank approximation to this matrix. The local low-rank construction is motivated by the nature of wave propagation and costs significantly less to apply than full exponentiati

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-Finite Elements with Decoupled Constraints for Elastoplasticityl basis functions for the discretization of a mixed formulation enables the decoupling of the constraints resulting from the involved plasticity functional. This yields a nonlinear equation which allows the application of various solution schemes, e.g. a semi-smooth Newton solver. Numerical experime

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Shape Optimization with Nonlinear Conjugate Gradient Methods methods as well as the corresponding theoretical background and investigate their performance numerically. The obtained results confirm that the NCG methods are efficient and attractive solution algorithms for shape optimization problems.

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