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Kormann, Katharina
Publikasjoner (10 av 22) Visa alla publikasjoner
Allmann-Rahn, F., Grauer, R. & Kormann, K. (2022). A parallel low-rank solver for the six-dimensional Vlasov-Maxwell equations. Journal of Computational Physics, 469, Article ID 111562.
Åpne denne publikasjonen i ny fane eller vindu >>A parallel low-rank solver for the six-dimensional Vlasov-Maxwell equations
2022 (engelsk)Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 469, artikkel-id 111562Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Continuum Vlasov simulations can be utilized for highly accurate modelling of fully kinetic plasmas. Great progress has been made recently regarding the applicability of the method in realistic plasma configurations. However, a reduction of the high computational cost that is inherent to fully kinetic simulations would be desirable, especially at high velocity space resolutions. For this purpose, low-rank approximations can be employed. The so far available low-rank solvers are restricted to either electrostatic systems or low dimensionality and can therefore not be applied to most space, astrophysical and fusion plasmas. In this paper we present a new parallel low-rank solver for the full six-dimensional electromagnetic Vlasov-Maxwell equations that can utilize distributed memory architectures. Special care is taken to ensure the conservation of mass and a good representation of Gauss's law. The low-rank Vlasov solver is applied to standard benchmark problems of plasma turbulence and magnetic reconnection and compared to the full grid method. It yields accurate results at significantly reduced computational cost.

sted, utgiver, år, opplag, sider
Elsevier, 2022
Emneord
Vlasov simulation, Kinetic plasmas, Low-rank approximation, Hierarchical Tucker decomposition, Tensor networks
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-487631 (URN)10.1016/j.jcp.2022.111562 (DOI)000862796900001 ()
Tilgjengelig fra: 2022-10-31 Laget: 2022-10-31 Sist oppdatert: 2022-10-31bibliografisk kontrollert
Pinto, M. C., Kormann, K. & Sonnendruecker, E. (2022). Variational Framework for Structure-Preserving Electromagnetic Particle-in-Cell Methods. Journal of Scientific Computing, 91(2), Article ID 46.
Åpne denne publikasjonen i ny fane eller vindu >>Variational Framework for Structure-Preserving Electromagnetic Particle-in-Cell Methods
2022 (engelsk)Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 91, nr 2, artikkel-id 46Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this article we apply a discrete action principle for the Vlasov-Maxwell equations in a structure-preserving particle-field discretization framework. In this framework the finite-dimensional electromagnetic potentials and fields are represented in a discrete de Rham sequence involving general finite element spaces, and the particle-field coupling is represented by a set of projection operators that commute with the differential operators. With a minimal number of assumptions which allow for a variety of finite elements and shape functions for the particles, we show that the resulting variational scheme has a general discrete Poisson structure and thus leads to a semi-discrete Hamiltonian system. By introducing discrete interior products we derive a second type of space discretization which is momentum preserving, based on the same finite elements and shape functions. We illustrate our method by applying it to spline finite elements, and to a new spectral discretization where the particle-field coupling relies on discrete Fourier transforms.

sted, utgiver, år, opplag, sider
Springer NatureSpringer Nature, 2022
Emneord
Vlasov-Maxwell, Particle-in-cell, Variational methods, Hamiltonian structure, Structure-preserving finite elements, Commuting de Rham diagram
HSV kategori
Forskningsprogram
Beräkningsvetenskap
Identifikatorer
urn:nbn:se:uu:diva-472745 (URN)10.1007/s10915-022-01781-3 (DOI)000776724800002 ()
Prosjekter
eSSENCE - An eScience Collaboration
Tilgjengelig fra: 2022-04-19 Laget: 2022-04-19 Sist oppdatert: 2024-01-15bibliografisk kontrollert
Munch, P., Kormann, K. & Kronbichler, M. (2021). hyper.deal: An Efficient, Matrix-free Finite-element Library for High-dimensional Partial Differential Equations. ACM Transactions on Mathematical Software, 47(4), 1-34, Article ID 33.
Åpne denne publikasjonen i ny fane eller vindu >>hyper.deal: An Efficient, Matrix-free Finite-element Library for High-dimensional Partial Differential Equations
2021 (engelsk)Inngår i: ACM Transactions on Mathematical Software, ISSN 0098-3500, E-ISSN 1557-7295, Vol. 47, nr 4, s. 1-34, artikkel-id 33Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

This work presents the efficient, matrix-free finite-element library hyper deal for solving partial differential equations in two up to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional finite-element library deal. II to create complex low-dimensional meshes and to operate on them individually. These meshes are combined via a tensor product on the fly, and the library provides new special-purpose highly optimized matrix-free functions exploiting domain decomposition as well as shared memory via MPI-3.0 features. Both node-level performance analyses and strong/weak-scaling studies on up to 147,456 CPU cores confirm the efficiency of the implementation. Results obtained with the library hyper . deal are reported for high-dimensional advection problems and for the solution of the Vlasov-Poisson equation in up to six-dimensional phase space.

sted, utgiver, år, opplag, sider
Association for Computing Machinery (ACM)ASSOC COMPUTING MACHINERY, 2021
Emneord
Matrix-free operator evaluation, discontinuous Galerkin methods, high-dimensional, high-order, Vlasov-Poisson equation, MPI-3.0 shared memory
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-457641 (URN)10.1145/3469720 (DOI)000703370900004 ()
Forskningsfinansiär
German Research Foundation (DFG), KO5206/1-1German Research Foundation (DFG), KR4661/2-1eSSENCE - An eScience Collaboration
Tilgjengelig fra: 2021-11-01 Laget: 2021-11-01 Sist oppdatert: 2024-01-15bibliografisk kontrollert
Nissen, A., Kormann, K., Grandin, M. & Virta, K. (2015). Stable difference methods for block-oriented adaptive grids. Journal of Scientific Computing, 65, 486-511
Åpne denne publikasjonen i ny fane eller vindu >>Stable difference methods for block-oriented adaptive grids
2015 (engelsk)Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 65, s. 486-511Artikkel i tidsskrift (Fagfellevurdert) Published
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-234977 (URN)10.1007/s10915-014-9969-z (DOI)000362911900003 ()
Prosjekter
eSSENCE
Tilgjengelig fra: 2014-12-18 Laget: 2014-10-27 Sist oppdatert: 2017-12-05bibliografisk kontrollert
Kormann, K. & Larsson, E. (2013). A Galerkin radial basis function method for the Schrödinger equation. SIAM Journal on Scientific Computing, 35, A2832-A2855
Åpne denne publikasjonen i ny fane eller vindu >>A Galerkin radial basis function method for the Schrödinger equation
2013 (engelsk)Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 35, s. A2832-A2855Artikkel i tidsskrift (Fagfellevurdert) Published
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-212482 (URN)10.1137/120893975 (DOI)000330028400018 ()
Prosjekter
eSSENCE
Tilgjengelig fra: 2013-12-05 Laget: 2013-12-10 Sist oppdatert: 2017-12-06bibliografisk kontrollert
Kronbichler, M. & Kormann, K. (2012). A generic interface for parallel cell-based finite element operator application. Computers & Fluids, 63, 135-147
Åpne denne publikasjonen i ny fane eller vindu >>A generic interface for parallel cell-based finite element operator application
2012 (engelsk)Inngår i: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 63, s. 135-147Artikkel i tidsskrift (Fagfellevurdert) Published
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-174401 (URN)10.1016/j.compfluid.2012.04.012 (DOI)000307093500010 ()
Prosjekter
eSSENCE
Tilgjengelig fra: 2012-04-21 Laget: 2012-05-15 Sist oppdatert: 2018-01-12bibliografisk kontrollert
Kormann, K. (2012). A time–space adaptive method for the Schrödinger equation.
Åpne denne publikasjonen i ny fane eller vindu >>A time–space adaptive method for the Schrödinger equation
2012 (engelsk)Rapport (Annet vitenskapelig)
Abstract [en]

In this paper, we present a discretization of the time-dependent Schrödinger equation based on a Magnus-Lanczos time integrator and high-order Gauss-Lobatto finite elements in space. A truncated Galerkin orthogonality is used to obtain duality-based a posteriori error estimates that address the temporal and the spatial error separately. Based on this theory, a space-time adaptive solver for the Schrödinger equation is devised. An efficient matrix-free implementation of the differential operator, suited for spectral elements, is used to enable computations for realistic configurations. We demonstrate the performance of the algorithm for the example of matter-field interaction.

Serie
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-023
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-180182 (URN)
Prosjekter
eSSENCE
Merknad

Updated 2012-09-12 (typos fixed).

Tilgjengelig fra: 2012-08-31 Laget: 2012-08-31 Sist oppdatert: 2024-05-30bibliografisk kontrollert
Kormann, K. & Larsson, E. (2012). An RBF–Galerkin approach to the time-dependent Schrödinger equation.
Åpne denne publikasjonen i ny fane eller vindu >>An RBF–Galerkin approach to the time-dependent Schrödinger equation
2012 (engelsk)Rapport (Annet vitenskapelig)
Abstract [en]

In this article, we consider the discretization of the time-dependent Schrödinger equation using radial basis functions (RBF). We formulate the discretized problem over an unbounded domain without imposing explicit boundary conditions. Since we can show that time-stability of the discretization is not guaranteed for an RBF-collocation method, we propose to employ a Galerkin ansatz instead. For Gaussians, it is shown that exponential convergence is obtained up to a point where a systematic error from the domain where no basis functions are centered takes over. The choice of the shape parameter and of the resolved region is studied numerically. Compared to the Fourier method with periodic boundary conditions, the basis functions can be centered in a smaller domain which gives increased accuracy with the same number of points.

Serie
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-024
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-180388 (URN)
Prosjekter
eSSENCE
Tilgjengelig fra: 2012-09-05 Laget: 2012-09-05 Sist oppdatert: 2024-05-30bibliografisk kontrollert
Gustafsson, M., Kormann, K. & Holmgren, S. (2012). Communication-efficient algorithms for numerical quantum dynamics. In: Applied Parallel and Scientific Computing: Part II. Paper presented at PARA 2010: State of the Art in Scientific and Parallel Computing (pp. 368-378). Berlin: Springer-Verlag
Åpne denne publikasjonen i ny fane eller vindu >>Communication-efficient algorithms for numerical quantum dynamics
2012 (engelsk)Inngår i: Applied Parallel and Scientific Computing: Part II, Berlin: Springer-Verlag , 2012, s. 368-378Konferansepaper, Publicerat paper (Fagfellevurdert)
sted, utgiver, år, opplag, sider
Berlin: Springer-Verlag, 2012
Serie
Lecture Notes in Computer Science ; 7134
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-135980 (URN)10.1007/978-3-642-28145-7_36 (DOI)000309716000036 ()978-3-642-28144-0 (ISBN)
Konferanse
PARA 2010: State of the Art in Scientific and Parallel Computing
Prosjekter
eSSENCEUPMARC
Tilgjengelig fra: 2012-02-16 Laget: 2010-12-09 Sist oppdatert: 2018-01-12bibliografisk kontrollert
Kormann, K., Kronbichler, M. & Müller, B. (2012). Derivation of strictly stable high order difference approximations for variable-coefficient PDE. Journal of Scientific Computing, 50, 167-197
Åpne denne publikasjonen i ny fane eller vindu >>Derivation of strictly stable high order difference approximations for variable-coefficient PDE
2012 (engelsk)Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 50, s. 167-197Artikkel i tidsskrift (Fagfellevurdert) Published
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-156537 (URN)10.1007/s10915-011-9479-1 (DOI)000298862000008 ()
Prosjekter
eSSENCE
Tilgjengelig fra: 2011-03-17 Laget: 2011-07-31 Sist oppdatert: 2017-12-08bibliografisk kontrollert
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