15 research outputs found
PACE solver description: tdULL
We describe tdULL, an algorithm for computing treedepth decompositions of minimal depth. An implementation was submitted to the exact track of PACE 2020. tdULL is a branch and bound algorithm branching on inclusion-minimal separators
Uniform preconditioners of linear complexity for problems of negative order
We propose a multi-level type operator that can be used in the framework of operator (or Caldéron) preconditioning to construct uniform preconditioners for negative order operators discretized by piecewise polynomials on a family of possibly locally refined partitions. The cost of applying this multi-level operator scales linearly in the number of mesh cells. Therefore, it provides a uniform preconditioner that can be applied in linear complexity when used within the preconditioning framework from our earlier work [Uniform preconditioners for problems of negative order, Math. Comp. 89 (2020), 645–674]
Adaptive space-time BEM for the heat equation
We consider the space-time boundary element method (BEM) for the heat
equation with prescribed initial and Dirichlet data. We propose a residual-type
a posteriori error estimator that is a lower bound and, up to weighted
-norms of the residual, also an upper bound for the unknown BEM error. The
possibly locally refined meshes are assumed to be prismatic, i.e., their
elements are tensor-products of elements in time and space .
While the results do not depend on the local aspect ratio between time and
space, assuming the scaling for all elements and
using Galerkin BEM, the estimator is shown to be efficient and reliable without
the additional -terms. In the considered numerical experiments on
two-dimensional domains in space, the estimator seems to be equivalent to the
error, independently of these assumptions. In particular for adaptive
anisotropic refinement, both converge with the best possible convergence rate