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Optimizing Geometric Multigrid Methods with Evolutionary Computation [article]

Jonas Schmitt, Sebastian Kuckuk, Harald Köstler
2019 arXiv   pre-print
Here we present a novel approach for the optimization of geometric multigrid methods that is based on evolutionary computation, a generic program optimization technique inspired by the principle of natural  ...  Based on these objectives a multi-objective optimization is performed using strongly typed genetic programming with a non-dominated sorting based selection.  ...  MULTI-OBJECTIVE OPTIMIZATION WITH EVOLUTIONARY COMPUTATION e fundamental requirement for the optimization of an iterative method is to have a way to evaluate both its rate of convergence and performance  ... 
arXiv:1910.02749v2 fatcat:i4rkb6qawngrrfieblu7sjckai

GPU acceleration for evolutionary topology optimization of continuum structures using isosurfaces

Jesús Martínez-Frutos, David Herrero-Pérez
2017 Computers & structures  
Evolutionary topology optimization of three-dimensional continuum structures is a computationally demanding task in terms of memory consumption and processing time.  ...  This work aims to alleviate these constraints proposing a well-suited strategy for Graphics Processing Unit (GPU) computing.  ...  Acknowledgment We gratefully acknowledge the support of NVIDIA Corporation with the donation of some of the GPUs used for this research.  ... 
doi:10.1016/j.compstruc.2016.10.018 fatcat:7hxl2vtzavdvvemndy5qrpb7ny

Multilevel strategies for parametric shape optimization in aerodynamics

Badr Abou El Majd, Jean-Antoine Désidéri, Régis Duvigneau
2008 European Journal of Computational Mechanics  
These methods employ nested parameterization supports of either shape, or shape deformation, and the classical process of degree elevation resulting in exact geometrical data transfer from coarse to fine  ...  The essential numerical features of multilevel strategies developed for parametric shape optimization are reviewed.  ...  , SQP, etc.); -robust optimizers for multi-modal or non-differentiable optimization problems (evolutionary computing: genetic or particle-swarm algorithms, etc.); and hybridization with deterministic optimizers  ... 
doi:10.13052/remn.17.149-168 fatcat:76sah2icrvgzjhh4bvtxhdiryi

Advanced Stencil-Code Engineering (Dagstuhl Seminar 15161)

Christian Lengauer, Matthias Bolten, Robert D. Falgout, Olaf Schenk, Marc Herbstritt
2015 Dagstuhl Reports  
The seminar was hosted by the DFG project with the same name (ExaStencils for short) in the DFG priority programme "Software for Exascale Computing" (SPPEXA).  ...  It brought together experts from mathematics, computer science and applications to explore the challenges of very high performance and massive parallelism in solving partial differential equations.  ...  This kind of mesh is suitable for the use with geometric multigrid methods and allows us to use stencil-based data structures which reduce the memory requirements drastically.  ... 
doi:10.4230/dagrep.5.4.56 dblp:journals/dagstuhl-reports/LengauerBFS15 fatcat:suk5zayvlnb63ozlamrw2vk2w4

3D topology optimization using an immune algorithm

Felipe Campelo, Kota Watanabe, Hajime Igarashi, Oszkar Biro
2007 Compel  
Findings -The proposed method is capable of finding an optimal configuration for the validation problem used.  ...  3D Topology Optimization Using an Immune Algorithm Abstract Purpose -The paper introduces an evolutionary algorithm based on the artificial immune systems paradigm for topology optimization in 3D.  ...  The multigrid method solves the given equations by successively performing this process. The geometric multi-grid method used in this work requires hierarchical meshes with different densities.  ... 
doi:10.1108/03321640710751145 fatcat:al5sruq6tvcn3dmih2vy4qjkge

Topology Optimization Based on Immune Algorithm and Multigrid Method

Kota Watanabe, F. Campelo, H. Igarashi
2007 IEEE transactions on magnetics  
Index Terms-Finite-element method (FEM), immune algorithm, multigrid method, topology optimization.  ...  This paper describes topology optimization of electromagnetic systems using the multigrid method.  ...  The geometric multigrid method, which is used in this work, requires the hierarchical meshes with different densities.  ... 
doi:10.1109/tmag.2006.892259 fatcat:rufzk6roabdf7imzpijx5a57aq

Efficient topology optimization using GPU computing with multilevel granularity

Jesús Martínez-Frutos, Pedro J. Martínez-Castejón, David Herrero-Pérez
2017 Advances in Engineering Software  
This paper proposes a well-suited strategy for High Performance Computing (HPC) of density-based topology optimization using Graphics Processing Units (GPUs).  ...  The proposal is also compared with the classical CPU implementation for diverse topology optimization problems, including stiffness maximization, heat sink design and compliant mechanism design.  ...  GPU computing is also used to increase the tractable computational resolution of topology optimization problems using discrete level-set methods [34] and evolutionary structural optimization methods  ... 
doi:10.1016/j.advengsoft.2017.01.009 fatcat:kstkbw5nebe2xhlqxyaug4z3we

Page 3579 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
Sachs, Flight path optimization with a new homotopy method for reduc- ing safety hazards in microbursts (189-197); R. Mehlhorn and G.  ...  Rentz-Reichert, Multigrid solution of the incompressible Navier-Stokes equations and its application to par- allel computers (51-60); M. Meinke, Th. Rister, F. Riitten and A.  ... 

ExaStencils: Advanced Multigrid Solver Generation [chapter]

Christian Lengauer, Sven Apel, Matthias Bolten, Shigeru Chiba, Ulrich Rüde, Jürgen Teich, Armin Größlinger, Frank Hannig, Harald Köstler, Lisa Claus, Alexander Grebhahn, Stefan Groth (+5 others)
2020 Lecture Notes in Computational Science and Engineering  
At every layer, the corresponding language expresses not only computational directives but also domain knowledge of the problem and platform to be leveraged for optimization.  ...  Project ExaStencils pursued a domain-specific approach with a language, called ExaSlang, that is stratified into four layers of abstraction, the most abstract being the formulation in continuous mathematics  ...  Acknowledgments Project ExaStencils received generous funding from the Deutsche Forschungsgemeinschaft (DFG) in its priority programme SPP 1648 "Software for Exascale Computing" under grant numbers AP  ... 
doi:10.1007/978-3-030-47956-5_14 fatcat:xhbxnt45ynhilgh6vv2ui2n76i

Morphing Wing Structural Optimization Using Opposite-Based Population-Based Incremental Learning and Multigrid Ground Elements

S. Sleesongsom, S. Bureerat
2015 Mathematical Problems in Engineering  
Firstly, a multigrid design approach for optimization of an unconventional morphing wing is proposed.  ...  Multiobjective design problems with single-grid and multigrid design variables are then posed and tackled by OMPBIL and MPBIL.  ...  The optimizer used herein is one of the most powerful evolutionary methods for solving structural topology optimization [11] .  ... 
doi:10.1155/2015/730626 fatcat:zkckpfetqbdldjfygmfjgsp7j4

Optimization-Based Algebraic Multigrid Coarsening Using Reinforcement Learning [article]

Ali Taghibakhshi, Scott MacLachlan, Luke Olson, Matthew West
2022 arXiv   pre-print
Algebraic multigrid (AMG) methods are one of the most common methods of solving such linear systems, with an extensive body of underlying mathematical theory.  ...  A system of linear equations defines a graph on the set of unknowns and each level of a multigrid solver requires the selection of an appropriate coarse graph along with restriction and interpolation operators  ...  [23] used evolutionary computation methods to optimize a GMG algorithm. By learning from supervised data and using a U-Net architecture, Hsieh et al.  ... 
arXiv:2106.01854v3 fatcat:2wz7eozrlfglfpi777zzzwyjpi

Page 1868 of Mathematical Reviews Vol. , Issue 89C [page]

1989 Mathematical Reviews  
N Open problems in communication and computation * 94003 Optimization of computations, and numerical methods * 65009 + 06001 *01003 * 00044 * 00023 * 62004 01071 01048 01064 01061 ,01093-01094 01068 01095  ...  for positional and programmed control oe : : * 49001 Some open questions in geometric topology and shape theory .  ... 

Evolutionary Black-box Topology Optimization: Challenges and Promises

David Guirguis, Carlos Artemio Coello Coello, Kazuhiro Saitou, Nikola Aulig, Renato Picelli, Bo Zhu, Yuqing Zhou, William Vicente, Francesco Iorio, Markus Olhofer, Wojciech Matusik
2019 IEEE Transactions on Evolutionary Computation  
Black-box topology optimization (BBTO) uses evolutionary algorithms and other soft computing techniques to generate near-optimal topologies of mechanical structures.  ...  Although evolutionary algorithms are widely used to compensate the limited applicability of conventional gradient optimization techniques, methods based on BBTO have been criticized due to numerous drawbacks  ...  Three types of representations for topology optimization with evolutionary computation [184] .  ... 
doi:10.1109/tevc.2019.2954411 fatcat:v72p6dsrvffmvimb3ajeifxskm

Improved formulation for geometric properties of arbitrary polyhedra

Z. J. Wang
1999 AIAA Journal  
For a computationalgrid with arbitrary polyhedral cells, such as cut cells generated through cell cutting in an adaptive Cartesian grid method, 1 it is not trivial to calculate the geometric properties  ...  This code employs total variation diminishingtype upwind differencing, 4 the lower-upper symmetric Gauss-Seidel scheme, and the multigrid method.  ... 
doi:10.2514/3.14325 fatcat:glzjel4ltbcztej76l7dvg3xdi

Improved Formulation for Geometric Properties of Arbitrary Polyhedra

Z. J. Wang
1999 AIAA Journal  
For a computationalgrid with arbitrary polyhedral cells, such as cut cells generated through cell cutting in an adaptive Cartesian grid method, 1 it is not trivial to calculate the geometric properties  ...  This code employs total variation diminishingtype upwind differencing, 4 the lower-upper symmetric Gauss-Seidel scheme, and the multigrid method.  ... 
doi:10.2514/2.604 fatcat:mr7vysk7zjeedc5ak7az7lntk4
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