An Open and Parallel Multiresolution Framework Using Block-Based Adaptive Grids

@article{Sroka2018AnOA,
  title={An Open and Parallel Multiresolution Framework Using Block-Based Adaptive Grids},
  author={Mario Sroka and Thomas Engels and Philipp Krah and S. Mutzel and Kai Schneider and Julius Reiss},
  journal={Notes on Numerical Fluid Mechanics and Multidisciplinary Design},
  year={2018}
}
  • M. Sroka, T. Engels, J. Reiss
  • Published 5 August 2018
  • Computer Science
  • Notes on Numerical Fluid Mechanics and Multidisciplinary Design
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and explicit time integration. Grid refinement and coarsening are triggered by multiresolution analysis, i.e. thresholding of wavelet coefficients, which allow controlling the precision of the adaptive approximation of the solution with respect to uniform grid… 

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References

SHOWING 1-10 OF 25 REFERENCES

Adaptive multiresolution methods

TLDR
These lecture notes present adaptive multiresolution schemes for evolutionary PDEs in Cartesian geometries based on Harten's approach for point and cell aver- ages and the sparse point representation method.

Comparison of Adaptive Multiresolution and Adaptive Mesh Refinement Applied to Simulations of the Compressible Euler Equations

TLDR
It is found that both approaches yield similar trends for CPU time compression for increasing number of refinement levels, and MR exhibits more efficient memory compression than AMR and shows slightly enhanced convergence; however, a larger absolute overhead is measured for the tested codes.

Adaptive multiresolution or adaptive mesh refinement? A case study for 2D Euler equations

TLDR
It is preliminarily concluded that the multiresolution techniques yield improved memory compression and gain in CPU time with respect to the adaptive mesh renement method.

Adaptive Multiresolution Computations Applied to Detonations

TLDR
A comparison of the adaptive scheme with reference computations on a regular grid allows to assess the accuracy and the computational efficiency, in terms of CPU time and memory requirements.

Multi-level adaptive solutions to boundary-value problems math comptr

TLDR
The boundary-value problem is discretized on several grids (or finite-element spaces) of widely different mesh sizes, enabling us to conveniently adapt the discretization to the evolving solution in a nearly optimal way, obtaining "°°-order" approximations and low n, even when singularities are present.

Adaptive mesh refinement for hyperbolic partial differential equations

TLDR
This work presents an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques based upon Richardson-type estimates of the truncation error, which is a mesh refinement algorithm in time and space.

Adaptive Multiresolution Methods: Practical issues on Data Structures, Implementation and Parallelization*

TLDR
The aim of the present work is to give a self-contained overview on the construction of an appropriate multiresolution analysis using biorthogonal wavelets, its efficient realization by means of hash maps using global cell identifiers and the parallelization of theMultiresolution-based grid adaptation via MPI using space-filling curves.

Block-structured Adaptive Mesh Refinement - Theory, Implementation and Application

TLDR
Large-scale simulations of shock-induced realistic combustion in non-Cartesian geometry and shock-driven fluid-structure interaction with fully coupled dynamic boundary motion demonstrate the applicability of the discussed techniques for complex scenarios.