Michael D. Multerer

TL;DR: Bembel as discussed by the authors is a C++ library featuring higher order Galerkin boundary element methods for Laplace, Helmholtz, and Maxwell problems for linear algebra operations.

TL;DR: In this article, the multilevel quadrature methods for parametric operator equations such as the multi-dimensional Monte Carlo method resemble a sparse tensor product approximation between the spatial variable and t.

TL;DR: Bembel is the C++ library featuring higher order isogeometric Galerkin boundary element methods for Laplace, Helmholtz, and Maxwell problems and provides an interface to the Eigen template library for linear algebra operations.

TL;DR: This work studies the numerical solution of forward and inverse acoustic scattering problems by randomly shaped obstacles in three-dimensional space using a fast isogeometric boundary element method and shows that the knowledge of the deformation field's expectation and covariance at the surface of the scatterer are already sufficient to compute the surface Karhunen-Loeve expansion.

TL;DR: A wavelet representation of the system matrix, yielding a quasi-sparse matrix, with the nested dissection ordering scheme is combined, yielding the exact inverse of the compressed system matrix with only a moderate increase of the number of nonzero entries in the matrix.