In this paper, we develop and analyze an efficient multigrid method to solve the finite element systems from elliptic obstacle problems on two dimensional adaptive meshes. Adaptive finite element methods (AFEMs) based on local mesh refinement are an important and efficient approach when the solution is non-smooth. An optimality theory on AFEM for linear elliptic equations can be found in Nochet...

Abstract This paper develops a method to flexibly adapt interpolation grids of value function approximations in the estimation dynamic models using either NFXP (Rust, Econometrica: Journal Econometric Society, 55, 999–1033, 1987) or MPEC (Su & Judd, Econometric 80, 2213–2230, 2012). Since requires grid structure for approximation be hard-coded into constraints, one cannot apply iterative...

Adaptive mesh refinement (AMR) is a state-of-the-art technique for the efficient numerical solution of partial differential equations (PDE) exhibiting multiple widely differing spatial scales. Recently, spacetree-based AMR has been established as a promising approach to structured AMR (see for example [1]). In the talk the integration of the two software modules PyClaw [2] and Peano [4] is pres...

Computational fluid dynamic (CFD) computations are memory and time intensive and need to be executed in parallel for larger computational domains. In order to produce physical accurate solutions, adaptive grid setups have to be chosen as the memory and computing time would otherwise be too high, and results would not be obtained in a reasonable amount of time. This paper describes the usage of ...

We study the efficient numerical simulation of laser surface remelting, a process to improve the surface quality of steel components. To this end we use adaptive grids, which are well-suited for problems with moving heat sources. To account for the local high activity due to the heat source, we introduce local uniform grids and couple the solutions on the global coarse and local fine grids usin...

Flow visualization tools based on particle methods continue to be an important utility of ow simulation. Additionally, sparse grids are of increasing interest in numerical simulations. In 13] we presented the advantages of particle tracing on uniform sparse grids. Here we present and compare two diierent approaches to accelerate particle tracing on sparse grids. Furthermore, a new approach is p...

In this paper we introduce an abstract data type for the distributed representation and eecient handling of sparse grids on parallel architectures. The new data layout, implemented by means of the PVM message passing library, provides partitioning and dynamic load balancing transparent to the application making use of it. This enables parallelization of sequential partial diierential equations ...

Sparse grids provide an eecient representation of discrete solutions of PDEs and are mainly based on speciic tensor products of 1D hierarchical basis ansatz functions. They easily allow adaptive reenement and coarsening. We present special nite diierences on sparse grids which possess nearly the same properties as nite diierences on full grids. Also higher order nite diierence operators on spar...