For the simple layer potential V that is associated with the 3D Laplacian, we consider the weakly singular integral equation V φ = f . This equation is discretized by the lowest order Galerkin boundary element method. We prove convergence of an h-adaptive algorithm that is driven by a weighted residual error estimator. Moreover, we identify the approximation class for which the adaptive algorit...

We describe a novel adaptive mesh representation for streak-surfaces. The surface is represented as a mesh of small trees of initial depth zero (treelets). This mesh representation allows for efficient integration, refinement, coarsening and appending of surface patches utilizing the computational capacities of modern GPUs. Integration, refinement, and rendering are strictly separated into effe...

Time-accurate fluid-structure interaction simulations of strong shock and detonation waves impinging on deforming solid structures benefit significantly from the application of dynamic mesh adaptation in the fluid. A patch-based parallel fluid solver with adaptive mesh refinement in space and time tailored for this problem class is presented; special attention is given to the robustness of the ...

We propose an adaptive mesh refinement strategy based on exploiting a combination of a pre–processing mesh re-distribution algorithm employing a harmonic mapping technique, and standard (isotropic) mesh subdivision for discontinuous Galerkin approximations of advection–diffusion problems. Numerical experiments indicate that the resulting adaptive strategy can efficiently reduce the computed dis...

We present first results obtained with a 3+1 dimensional adaptive mesh code in numerical general relativity. The adaptive mesh is used in conjunction with a standard ADM code for the evolution of a dynamically sliced Schwarzschild spacetime (geodesic slicing). We argue that adaptive mesh is particularly natural in the context of general relativity, where apart from adaptive mesh refinement for ...