Cached Gaussian elimination for simulating Stokes flow on domains with repetitive geometry
•Specialized efficient solver for fluids for microfluidics applications.•Solves Stokes equations with one million degrees of freedom in one second.•Special solver for sparse symmetric indefinite systems of linear equations.•Formally third order accurate in velocity and second order accurate in press...
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| Vydané v: | Journal of computational physics Ročník 423; s. 109812 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Cambridge
Elsevier Inc
15.12.2020
Elsevier Science Ltd |
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| ISSN: | 0021-9991, 1090-2716 |
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| Abstract | •Specialized efficient solver for fluids for microfluidics applications.•Solves Stokes equations with one million degrees of freedom in one second.•Special solver for sparse symmetric indefinite systems of linear equations.•Formally third order accurate in velocity and second order accurate in pressure.
Microfluidic “lab on a chip” devices are small devices that operate on small length scales on small volumes of fluid; these devices find uses in a variety of applications. Designs for microfluidic chips are generally composed of standardized and often repeated components connected by long, thin, straight fluid channels. We propose a novel meshing algorithm for use in simulating the linear incompressible stationary Stokes equations on geometry with these features, which produces sparse symmetric positive indefinite systems with many repeated matrix blocks. We use a discretization that is formally third order accurate for velocity and second order accurate for pressure in the L∞ norm. We also propose a novel linear system solver based on cyclic reduction, reordered sparse Gaussian elimination, and operation caching that is designed to efficiently solve systems with repeated matrix blocks. We demonstrate that the resulting fluid solver is significantly faster than existing methods up to resolutions of a few million degrees of freedom for microfluidic problems. |
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| AbstractList | Microfluidic "lab on a chip" devices are small devices that operate on small length scales on small volumes of fluid; these devices find uses in a variety of applications. Designs for microfluidic chips are generally composed of standardized and often repeated components connected by long, thin, straight fluid channels. We propose a novel meshing algorithm for use in simulating the linear incompressible stationary Stokes equations on geometry with these features, which produces sparse symmetric positive indefinite systems with many repeated matrix blocks. We use a discretization that is formally third order accurate for velocity and second order accurate for pressure in the L∞ norm. We also propose a novel linear system solver based on cyclic reduction, reordered sparse Gaussian elimination, and operation caching that is designed to efficiently solve systems with repeated matrix blocks. We demonstrate that the resulting fluid solver is significantly faster than existing methods up to resolutions of a few million degrees of freedom for microfluidic problems. •Specialized efficient solver for fluids for microfluidics applications.•Solves Stokes equations with one million degrees of freedom in one second.•Special solver for sparse symmetric indefinite systems of linear equations.•Formally third order accurate in velocity and second order accurate in pressure. Microfluidic “lab on a chip” devices are small devices that operate on small length scales on small volumes of fluid; these devices find uses in a variety of applications. Designs for microfluidic chips are generally composed of standardized and often repeated components connected by long, thin, straight fluid channels. We propose a novel meshing algorithm for use in simulating the linear incompressible stationary Stokes equations on geometry with these features, which produces sparse symmetric positive indefinite systems with many repeated matrix blocks. We use a discretization that is formally third order accurate for velocity and second order accurate for pressure in the L∞ norm. We also propose a novel linear system solver based on cyclic reduction, reordered sparse Gaussian elimination, and operation caching that is designed to efficiently solve systems with repeated matrix blocks. We demonstrate that the resulting fluid solver is significantly faster than existing methods up to resolutions of a few million degrees of freedom for microfluidic problems. |
| ArticleNumber | 109812 |
| Author | Schroeder, Craig Ding, Ounan |
| Author_xml | – sequence: 1 givenname: Ounan orcidid: 0000-0001-6067-4582 surname: Ding fullname: Ding, Ounan – sequence: 2 givenname: Craig orcidid: 0000-0003-0528-7007 surname: Schroeder fullname: Schroeder, Craig email: craigs@cs.ucr.edu |
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| CitedBy_id | crossref_primary_10_1016_j_compfluid_2024_106421 |
| Cites_doi | 10.1016/j.cej.2007.07.047 10.2514/3.25233 10.1145/992200.992206 10.1007/s10915-011-9549-4 10.1145/2980179.2982430 10.1371/journal.pone.0189429 10.1145/992200.992205 10.1016/j.compfluid.2013.06.024 10.1016/j.icheatmasstransfer.2012.06.013 10.1007/BF01399555 10.1002/nme.1620020104 10.1007/s10404-016-1842-y 10.1145/3313867 10.1177/1094342016671790 10.1016/j.jcp.2014.01.051 10.1007/s10404-014-1502-z 10.1145/356044.356047 10.1016/j.compfluid.2007.07.014 10.1137/1019071 10.1137/0712047 10.1090/S0025-5718-1966-0234618-4 10.1002/nme.1620100209 10.1016/0743-7315(92)90012-C 10.1016/j.jcp.2013.04.041 10.1137/0910069 10.1137/0907058 10.1016/0167-8191(86)90019-0 10.1145/355656.355658 10.1039/b912547g 10.1016/j.parco.2005.07.004 10.1007/BF01396361 10.1137/1031001 10.1137/0613024 10.1137/0707049 10.1137/0713042 10.1017/S0962492916000076 10.1016/j.jcp.2006.11.023 10.1007/s10404-012-0940-8 10.1145/321250.321259 10.1137/0710032 10.1007/BF01389450 10.1145/361604.361619 10.1039/C6LC00758A 10.1145/76909.76910 10.1002/nme.1620290712 10.1145/1024074.1024080 10.1115/1.1436090 10.1137/S0895479894246905 10.1145/1837853.1693472 10.1137/S0895479899358194 10.1016/S0045-7825(99)00242-X 10.2514/3.9975 10.1016/0021-9991(82)90058-4 |
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| Keywords | Cyclic reduction Sparse direct solver Microfluidics Stokes flow |
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| Snippet | •Specialized efficient solver for fluids for microfluidics applications.•Solves Stokes equations with one million degrees of freedom in one second.•Special... Microfluidic "lab on a chip" devices are small devices that operate on small length scales on small volumes of fluid; these devices find uses in a variety of... |
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| SubjectTerms | Algorithms Caching Computational physics Cyclic reduction Fluid dynamics Fluid flow Gaussian elimination Incompressible flow Mathematical analysis Matrix methods Microfluidics Solvers Sparse direct solver Stokes flow |
| Title | Cached Gaussian elimination for simulating Stokes flow on domains with repetitive geometry |
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