A massively parallel geometric multigrid solver on hierarchically distributed grids

2013 ◽  
Vol 16 (4) ◽  
pp. 151-164 ◽  
Author(s):  
Sebastian Reiter ◽  
Andreas Vogel ◽  
Ingo Heppner ◽  
Martin Rupp ◽  
Gabriel Wittum
Keyword(s):  
Massively Parallel ◽  
Multigrid Solver ◽  
Geometric Multigrid

A Geometric Multigrid Solver on Tsubame 2.0

2014 ◽  
pp. 155-173 ◽  
Author(s):  
Harald Köstler ◽  
Christian Feichtinger ◽  
Ulrich Rüde ◽  
Takayuki Aoki
Keyword(s):  
Multigrid Solver ◽  
Geometric Multigrid

scholarly journals EvoStencils: a grammar-based genetic programming approach for constructing efficient geometric multigrid methods

2021 ◽  
Author(s):  
Jonas Schmitt ◽  
Sebastian Kuckuk ◽  
Harald Köstler
Keyword(s):  
Genetic Programming ◽  
Code Generation ◽  
Performance Metrics ◽  
Linear Equations ◽  
Optimization Technique ◽  
Multigrid Methods ◽  
Programming Approach ◽  
Program Optimization ◽  
Multigrid Solver ◽  
Geometric Multigrid

AbstractFor many systems of linear equations that arise from the discretization of partial differential equations, the construction of an efficient multigrid solver is challenging. Here we present EvoStencils, a novel approach for optimizing geometric multigrid methods with grammar-guided genetic programming, a stochastic program optimization technique inspired by the principle of natural evolution. A multigrid solver is represented as a tree of mathematical expressions that we generate based on a formal grammar. The quality of each solver is evaluated in terms of convergence and compute performance by automatically generating an optimized implementation using code generation that is then executed on the target platform to measure all relevant performance metrics. Based on this, a multi-objective optimization is performed using a non-dominated sorting-based selection. To evaluate a large number of solvers in parallel, they are distributed to multiple compute nodes. We demonstrate the effectiveness of our implementation by constructing geometric multigrid solvers that are able to outperform hand-crafted methods for Poisson’s equation and a linear elastic boundary value problem with up to 16 million unknowns on multi-core processors with Ivy Bridge and Broadwell microarchitecture.

Simulation and optimization of Al–Fe aerospace alloy processed by laser surface remelting using geometric Multigrid solver and experimental validation

2015 ◽  
Vol 52 (5) ◽  
pp. 1037-1049 ◽  
Author(s):  
Moisés Meza Pariona ◽  
Fabiane de Oliveira ◽  
Viviane Teleginski ◽  
Siliane Machado ◽  
Marcio Augusto Villela Pinto
Keyword(s):  
Experimental Validation ◽  
Laser Surface ◽  
Multigrid Solver ◽  
Simulation And Optimization ◽  
Laser Surface Remelting ◽  
Geometric Multigrid

scholarly journals A shape optimization algorithm for cellular composites

2021 ◽  
Keyword(s):  
Shape Optimization ◽  
Optimization Algorithm ◽  
Elastic Energy ◽  
Inner Product ◽  
Mesh Deformation ◽  
Multigrid Solver ◽  
Parallel Scalability ◽  
Shape Spaces ◽  
Linear Elastic ◽  
Geometric Multigrid

We propose and investigate a mesh deformation technique for PDE constrained shape optimization. Introducing a gradient penalization to the inner product for linearized shape spaces, mesh degeneration can be prevented within the optimization iteration allowing for the scalability of employed solvers. We illustrate the approach by a shape optimization for cellular composites with respect to linear elastic energy under tension. The influence of the gradient penalization is evaluated and the parallel scalability of the approach demonstrated employing a geometric multigrid solver on hierarchically distributed meshes.

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