scholarly journals Parallel Adaptive Mesh Refinement Combined with Additive Multigrid for the Efficient Solution of the Poisson Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Hua Ji ◽  
Fue-Sang Lien ◽  
Eugene Yee
Keyword(s):  
Data Structure ◽  
Poisson Equation ◽  
Adaptive Mesh Refinement ◽  
Multigrid Method ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Space Filling Curve ◽  
Grid Partitioning ◽  
Highly Efficient ◽  
The Poisson Equation

Three different speed-up methods (viz., additive multigrid method, adaptive mesh refinement (AMR), and parallelization) have been combined in order to provide a highly efficient parallel solver for the Poisson equation. Rather than using an ordinary tree data structure to organize the information on the adaptive Cartesian mesh, a modified form of the fully threaded tree (FTT) data structure is used. The Hilbert space-filling curve (SFC) approach has been adopted for dynamic grid partitioning (resulting in a partitioning that is near optimal with respect to load balancing on a parallel computational platform). Finally, an additive multigrid method (BPX preconditioner), which itself is parallelizable to a certain extent, has been used to solve the linear equation system arising from the discretization. Our numerical experiments show that the proposed parallel AMR algorithm based on the FTT data structure, Hilbert SFC for grid partitioning, and additive multigrid method is highly efficient.

Multigrid upwind Euler/Navier-Stokes computation on adaptive unstructured meshes

2001 ◽  
Vol 105 (1046) ◽  
pp. 173-184 ◽  
Author(s):  
Y. Zheng ◽  
L. He
Keyword(s):  
Adaptive Mesh Refinement ◽  
Multigrid Method ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Navier Stokes ◽  
Steady Flows ◽  
Flow Solver ◽  
Solution Convergence ◽  
Time Marching ◽  
Accuracy Speed

Abstract An unstructured flow solver with adaptive mesh refinement and multigrid acceleration is developed to efficiently compute two-dimensional inviscid and viscous steady flows about complex configurations. High resolution is achieved by using the upwind scheme coupled with adaptive mesh refinement. An aspect-ratio adaptive multigrid method is developed and applied to effectively accelerate the solution convergence of the explicit time-marching in the near wall regions with high aspect mesh ratios. Numerical examples are presented for configurations and conditions ranging from transonic to low speed flows to demonstrate accuracy, speed, and robustness of the method.

Adaptive Mesh Refinement in 2D – An Efficient Implementation in Matlab

2020 ◽  
Vol 20 (3) ◽  
pp. 459-479 ◽  
Author(s):  
Stefan A. Funken ◽  
Anja Schmidt
Keyword(s):  
Data Structure ◽  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Two Dimensions ◽  
Efficient Implementation ◽  
Research And Education ◽  
Mesh Refinements ◽  
Implementation In Matlab

AbstractThis paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab. We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-in functions and vectorization. This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab. Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use. Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education.

Numerical simulations of acoustic waves with the graphic acceleration GAMER code

2012 ◽  
Vol 60 (4) ◽  
pp. 787-792
Author(s):  
K. Murawski ◽  
K. Murawski ◽  
H.-Y. Schive
Keyword(s):  
Data Structure ◽  
Numerical Simulations ◽  
Acoustic Waves ◽  
Adaptive Mesh Refinement ◽  
Spatial Scales ◽  
Adaptive Mesh ◽  
Processing Unit ◽  
Space Filling Curve ◽  
Central Processing ◽  
Amplitude Growth

Abstract We present results of numerical simulations of acoustic waves with the use of the Graphics Processing Unit (GPU) acceleration GAMER code which implements a second-order Godunov-type numerical scheme and adaptive mesh refinement (AMR). The AMR implementation is based on constructing a hierarchy of grid patches with an octree data structure. In this code a hybrid model is adopted, in which the time-consuming solvers are dealt with GPUs and the complex AMR data structure is manipulated by Central Processing Units (CPUs). The code is highly parallelized with the Hilbert space-filling curve method. These implementations allow us to resolve well desperate spatial scales that are associated with acoustic waves. We show that a localized velocity (gas pressure) pulse that is initially launched within a uniform and still medium triggers acoustic waves simultaneously with a vortex (an entropy mode). In a flowing medium, acoustic waves experience amplitude growth or decay, a scenario which depends on a location of the flow and relative direction of wave propagation. The amplitude growth results from instabilities which are associated with negative energy waves.

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