Adaptive space-time BEM for the heat equation

Fast Adaptive Methods for the Free-Space Heat Equation

A Geometric Space-Time Multigrid Algorithm for the Heat Equation

We study the time-dependent heat equation on its space-time domain that is discretised by a k-spacetree. k-spacetrees are a generalisation of the octree concept and are a discretisation paradigm yielding a multiscale representation of dynamically adaptive Cartesian grids with low memory footprint. The paper presents a full approximation storage geometric multigrid implementation for this settin...

A numerical scheme for space-time fractional advection-dispersion equation

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...

A time-space adaptive method for the Schrödinger equation

In this paper, we present a discretization of the time-dependent Schrödinger equation based on a Magnus–Lanczos time integrator and high-order Gauss– Lobatto finite elements in space. A truncated Galerkin orthogonality is used to obtain duality-based a posteriori error estimates that address the temporal and the spatial error separately. Based on this theory, a space-time adaptive solver for th...

Adaptive Unstructured Grid Generation Scheme for Solution of the Heat Equation

An adaptive unstructured grid generation scheme is introduced to use finite volume (FV) and finite element (FE) formulation to solve the heat equation with singular boundary conditions. Regular grids could not acheive accurate solution to this problem. The grid generation scheme uses an optimal time complexity frontal method for the automatic generation and delaunay triangulation of the grid po...