A fast direct solver for nonlocal operators in wavelet coordinates

In this article, we consider fast direct solvers for nonlocal operators. The pivotal idea is to combine a wavelet representation of the system matrix, yielding quasi-sparse with nested dissection ordering scheme. latter drastically reduces fill-in during factorization matrix by means Cholesky decomposition or an LU decomposition, respectively. This way, end up exact inverse compressed only moderate increase number nonzero entries in matrix. To illustrate efficacy approach, conduct numerical experiments different highly relevant applications operators: We (i) solution boundary integral equations three spatial dimensions, issuing from polarizable continuum model, (ii) parabolic problem fractional Laplacian form and (iii) simulation Gaussian random fields.