Sparse Jacobian construction for mapped grid visco-resistive magnetohydrodynamics

Handle URI:
http://hdl.handle.net/10754/564491
Title:
Sparse Jacobian construction for mapped grid visco-resistive magnetohydrodynamics
Authors:
Reynolds, Daniel R.; Samtaney, Ravi ( 0000-0002-4702-6473 )
Abstract:
We apply the automatic differentiation tool OpenAD toward constructing a preconditioner for fully implicit simulations of mapped grid visco-resistive magnetohydrodynamics (MHD), used in modeling tokamak fusion devices. Our simulation framework employs a fully implicit formulation in time, and a mapped finite volume spatial discretization. We solve this model using inexact Newton-Krylov methods. Of critical importance in these iterative solvers is the development of an effective preconditioner, which typically requires knowledge of the Jacobian of the nonlinear residual function. However, due to significant nonlinearity within our PDE system, our mapped spatial discretization, and stencil adaptivity at physical boundaries, analytical derivation of these Jacobian entries is highly nontrivial. This paper therefore focuses on Jacobian construction using automatic differentiation. In particular, we discuss applying OpenAD to the case of a spatially-adaptive stencil patch that automatically handles differences between the domain interior and boundary, and configuring AD for reduced stencil approximations to the Jacobian. We investigate both scalar and vector tangent mode differentiation, along with simple finite difference approaches, to compare the resulting accuracy and efficiency of Jacobian construction in this application. © 2012 Springer-Verlag.
KAUST Department:
Mechanical Engineering Program; Physical Sciences and Engineering (PSE) Division; Clean Combustion Research Center; Fluid and Plasma Simulation Group (FPS)
Publisher:
Springer Science + Business Media
Journal:
Lecture Notes in Computational Science and Engineering
Conference/Event name:
6th International Conference on Automatic Differentiation, AD 2012
Issue Date:
2012
DOI:
10.1007/978-3-642-30023-3_2
Type:
Conference Paper
ISSN:
14397358
ISBN:
9783642300226
Appears in Collections:
Conference Papers; Physical Sciences and Engineering (PSE) Division; Mechanical Engineering Program; Clean Combustion Research Center

Full metadata record

DC FieldValue Language
dc.contributor.authorReynolds, Daniel R.en
dc.contributor.authorSamtaney, Ravien
dc.date.accessioned2015-08-04T07:02:21Zen
dc.date.available2015-08-04T07:02:21Zen
dc.date.issued2012en
dc.identifier.isbn9783642300226en
dc.identifier.issn14397358en
dc.identifier.doi10.1007/978-3-642-30023-3_2en
dc.identifier.urihttp://hdl.handle.net/10754/564491en
dc.description.abstractWe apply the automatic differentiation tool OpenAD toward constructing a preconditioner for fully implicit simulations of mapped grid visco-resistive magnetohydrodynamics (MHD), used in modeling tokamak fusion devices. Our simulation framework employs a fully implicit formulation in time, and a mapped finite volume spatial discretization. We solve this model using inexact Newton-Krylov methods. Of critical importance in these iterative solvers is the development of an effective preconditioner, which typically requires knowledge of the Jacobian of the nonlinear residual function. However, due to significant nonlinearity within our PDE system, our mapped spatial discretization, and stencil adaptivity at physical boundaries, analytical derivation of these Jacobian entries is highly nontrivial. This paper therefore focuses on Jacobian construction using automatic differentiation. In particular, we discuss applying OpenAD to the case of a spatially-adaptive stencil patch that automatically handles differences between the domain interior and boundary, and configuring AD for reduced stencil approximations to the Jacobian. We investigate both scalar and vector tangent mode differentiation, along with simple finite difference approaches, to compare the resulting accuracy and efficiency of Jacobian construction in this application. © 2012 Springer-Verlag.en
dc.publisherSpringer Science + Business Mediaen
dc.subjectForward modeen
dc.subjectIterative methodsen
dc.subjectSparse Jacobian constructionen
dc.titleSparse Jacobian construction for mapped grid visco-resistive magnetohydrodynamicsen
dc.typeConference Paperen
dc.contributor.departmentMechanical Engineering Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentClean Combustion Research Centeren
dc.contributor.departmentFluid and Plasma Simulation Group (FPS)en
dc.identifier.journalLecture Notes in Computational Science and Engineeringen
dc.conference.date23 July 2012 through 27 July 2012en
dc.conference.name6th International Conference on Automatic Differentiation, AD 2012en
dc.conference.locationFort Collins, COen
dc.contributor.institutionDepartment of Mathematics, Southern Methodist University, Dallas, TX 75275, United Statesen
kaust.authorSamtaney, Ravien
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