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{"id":336,"date":"2019-07-21T21:13:00","date_gmt":"2019-07-21T21:13:00","guid":{"rendered":"http:\/\/numbox.it4i.cz\/?page_id=336"},"modified":"2019-08-26T18:56:54","modified_gmt":"2019-08-26T18:56:54","slug":"solver","status":"publish","type":"page","link":"https:\/\/numbox.it4i.cz\/homepage\/espreso-features\/solver\/","title":{"rendered":"Solvers"},"content":{"rendered":"\t\t
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Massively Parallel Solvers<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Designed to take full advantage of today's\u200b most powerful petascale supercomputers <\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Iterative<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Parallel sparse linear solver<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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The ESPRESO framework contains several highly scalable solvers based on the methods of domain decomposition which allows the computational capacity of the state-of-the-art supercomputers to be fully utilized and thus solve problems with billions of unknowns.<\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\n\t\t\t\t\t\tfor Massively Parallel systems\t\t\t\t\t<\/p>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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\n\t\t\t\t\t\n\t\t\t\t\t\tGPU version\t\t\t\t\t<\/span>\n\t\t\t\t<\/h3>\n\t\t\t\t\t\t\t\t\t

\n\t\t\t\t\t\tNvidia GPU accelerated version for systems with hybrid architectures\n\t\t\t\t\t<\/p>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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\n\t\t\t\t\t\n\t\t\t\t\t\tAutomatic tuning \t\t\t\t\t<\/span>\n\t\t\t\t<\/h3>\n\t\t\t\t\t\t\t\t\t

\n\t\t\t\t\t\tsolver setting by evolutionary and swarm optimisation algorithms\t\t\t\t\t<\/p>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Strong scalability - elasticity problem<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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\"\"<\/figure>

300 Million unknowns Jet Engine case<\/h3><\/div><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Successfully Tested on large Peta-scale \nmachines<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Largest problem solved by ESPRESO <\/b>in 160 seconds<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Billion unknowns<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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#CPU Cores<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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The ESPRESO solver is an in-house developed highly efficient parallel solver that contains several FETI based algorithms including the Hybrid Total FETI method suitable for parallel machines with tens or hundreds of thousands of cores. The solver is based on a highly efficient communication layer on top of MPI. It is not just an MPI code but, as many modern parallel applications, it uses the hybrid parallelization. The three levels of parallelization are message passing, threading using OpenMP, and vectorization using Intel MKL and OpenMP.<\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Hybrid solver strong scalability<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Heat transfer<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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20 billion unknowns <\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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Elasticity<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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11 bilion unknowns<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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We also offer our massively parallel solver as a third party library. To interface ESPRESO with the third party software, a general API has been implemented. The API has been successfully used to connect ESPRESO with the Elmer<\/a>. Even though ESPRESO is C++ library, the API uses plain C only. Hence, it is easy to use it with various other languages such as Fortran.<\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Quadratic programming<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Scalable nonlinear solvers<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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For nonlinear problems with equality and inequality conditions, we implement an in-house solver based on quadratic programming problems. This solver in combination with domain decomposition techniques gives users the possibility to solve contact problems in parallel with almost linear complexity<\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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semi-monotonic augmented Lagrangian method with separable convex constraints and general equality constraints<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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modified proportioning with reduced gradient projection<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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In-house constrained QP algorithm<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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We combine an augmented Lagrangian based solver with active set reflecting restarted preconditioned conjugate gradients in the inner loop, and FETI based domain decomposition techniques. Consequently we are able to solve especially large contact problems efficiently on HPC infrastructures.<\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Available third party solvers<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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For highly heterogenous systems, algebraic multigrid or direct solvers can be used for solving defined problems.<\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\n\t\t\t\t\t\n\t\t\t\t\t\tMultigrid based iterative solver\t\t\t\t\t<\/span>\n\t\t\t\t<\/h3>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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\n\t\t\t\t\t\n\t\t\t\t\t\tmulti-core and multi-node parallel direct solvers \t\t\t\t\t<\/span>\n\t\t\t\t<\/h3>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

Massively Parallel Solvers Designed to take full advantage of today’s\u200b most powerful petascale supercomputers Iterative Parallel sparse linear solver The ESPRESO framework contains several highly scalable solvers based on the methods of domain decomposition which allows the computational capacity of the state-of-the-art supercomputers to be fully utilized and thus solve problems with billions of unknowns. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1091,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/numbox.it4i.cz\/wp-json\/wp\/v2\/pages\/336"}],"collection":[{"href":"https:\/\/numbox.it4i.cz\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/numbox.it4i.cz\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/numbox.it4i.cz\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/numbox.it4i.cz\/wp-json\/wp\/v2\/comments?post=336"}],"version-history":[{"count":30,"href":"https:\/\/numbox.it4i.cz\/wp-json\/wp\/v2\/pages\/336\/revisions"}],"predecessor-version":[{"id":1297,"href":"https:\/\/numbox.it4i.cz\/wp-json\/wp\/v2\/pages\/336\/revisions\/1297"}],"up":[{"embeddable":true,"href":"https:\/\/numbox.it4i.cz\/wp-json\/wp\/v2\/pages\/1091"}],"wp:attachment":[{"href":"https:\/\/numbox.it4i.cz\/wp-json\/wp\/v2\/media?parent=336"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}