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Almquist, Martinorcid.org/0000-0002-8012-5860

Open this publication in new window or tab >>Order-preserving interpolation for summation-by-parts operators at nonconforming grid interfaces### Almquist, Martin

### Wang, Siyang

### Werpers, Jonatan

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##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-387569 (URN)10.1137/18M1191609 (DOI)000469225300021 ()
#####

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Available from: 2019-04-18 Created: 2019-06-24 Last updated: 2019-06-24Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Open this publication in new window or tab >>Boundary optimized diagonal-norm SBP operators### Mattsson, Ken

### Almquist, Martin

### van der Weide, Edwin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 374, p. 1261-1266Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-354575 (URN)10.1016/j.jcp.2018.06.010 (DOI)000447904200059 ()
#####

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Available from: 2018-06-05 Created: 2018-06-20 Last updated: 2019-06-27Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Open this publication in new window or tab >>A high-order accurate embedded boundary method for first order hyperbolic equations### Mattsson, Ken

### Almquist, Martin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 334, p. 255-279Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-310122 (URN)10.1016/j.jcp.2016.12.034 (DOI)000395210500015 ()
#####

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Available from: 2016-12-28 Created: 2016-12-11 Last updated: 2017-06-30Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Open this publication in new window or tab >>Efficient Simulation of Wave Phenomena### Almquist, Martin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2017 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis, 2017. p. 42
##### Series

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1463
##### Keywords

finite difference method, high-order accuracy, stability, summation by parts, simultaneous approximation term, quantum mechanics, Dirac equation, local time-stepping
##### National Category

Computational Mathematics
##### Research subject

Scientific Computing with specialization in Numerical Analysis
##### Identifiers

urn:nbn:se:uu:diva-310124 (URN)978-91-554-9777-4 (ISBN)
##### Public defence

2017-02-10, Room 2446, ITC, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
##### Opponent

### Iaccarino, Gianluca

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##### Supervisors

### Mattsson, Ken

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Available from: 2017-01-19 Created: 2016-12-11 Last updated: 2017-01-25

Wave phenomena appear in many fields of science such as acoustics, geophysics, and quantum mechanics. They can often be described by partial differential equations (PDEs). As PDEs typically are too difficult to solve by hand, the only option is to compute approximate solutions by implementing numerical methods on computers. Ideally, the numerical methods should produce accurate solutions at low computational cost. For wave propagation problems, high-order finite difference methods are known to be computationally cheap, but historically it has been difficult to construct stable methods. Thus, they have not been guaranteed to produce reasonable results.

In this thesis we consider finite difference methods on summation-by-parts (SBP) form. To impose boundary and interface conditions we use the simultaneous approximation term (SAT) method. The SBP-SAT technique is designed such that the numerical solution mimics the energy estimates satisfied by the true solution. Hence, SBP-SAT schemes are energy-stable by construction and guaranteed to converge to the true solution of well-posed linear PDE. The SBP-SAT framework provides a means to derive high-order methods without jeopardizing stability. Thus, they overcome most of the drawbacks historically associated with finite difference methods.

This thesis consists of three parts. The first part is devoted to improving existing SBP-SAT methods. In Papers I and II, we derive schemes with improved accuracy compared to standard schemes. In Paper III, we present an embedded boundary method that makes it easier to cope with complex geometries. The second part of the thesis shows how to apply the SBP-SAT method to wave propagation problems in acoustics (Paper IV) and quantum mechanics (Papers V and VI). The third part of the thesis, consisting of Paper VII, presents an efficient, fully explicit time-integration scheme well suited for locally refined meshes.

Center for Turbulence Research, Department of Mechanical Engineering, Stanford University.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.

Open this publication in new window or tab >>Multilevel local time-stepping methods of Runge–Kutta-type for wave equations### Almquist, Martin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Mehlin, Michaela

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, p. A2020-A2048Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-310123 (URN)10.1137/16M1084407 (DOI)000415797300064 ()
#####

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Available from: 2017-09-14 Created: 2016-12-11 Last updated: 2018-03-02Bibliographically approved

Open this publication in new window or tab >>Realization of adiabatic Aharonov–Bohm scattering with neutrons### Sjöqvist, Erik

### Almquist, Martin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Mattsson, Ken

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Gürkan, Zeynep Nilhan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); ### Hessmo, Björn

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_5_j_idt188_j_idt202",{id:"formSmash:j_idt184:5:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2015 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 92, no 5, p. 052108:1-5, article id 052108Article in journal (Refereed) Published
##### National Category

Atom and Molecular Physics and Optics Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-246721 (URN)10.1103/PhysRevA.92.052108 (DOI)000364468300002 ()
#####

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##### Funder

Swedish Research Council, D0413201
Available from: 2015-11-12 Created: 2015-03-09 Last updated: 2017-12-04Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.

Open this publication in new window or tab >>Unsteady simulations of rotor stator interactions using SBP-SAT schemes: Status and challenges### Giangaspero, Giorgio

### Almquist, Martin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Mattsson, Ken

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### van der Weide, Edwin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Spectral and High Order Methods for Partial Differential Equations: ICOSAHOM 2014, Springer, 2015, p. 247-255Conference paper, Published paper (Refereed)
##### Place, publisher, year, edition, pages

Springer, 2015
##### Series

Lecture Notes in Computational Science and Engineering ; 106
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-281562 (URN)10.1007/978-3-319-19800-2_21 (DOI)000368440400021 ()978-3-319-19799-9 (ISBN)
##### Conference

ICOSAHOM 2014
#####

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Available from: 2015-03-24 Created: 2016-03-24 Last updated: 2016-03-31Bibliographically approved

Open this publication in new window or tab >>Atmospheric sound propagation over large-scale irregular terrain### Almquist, Martin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Karasalo, Ilkka

### Mattsson, Ken

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2014 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, p. 369-397Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-218680 (URN)10.1007/s10915-014-9830-4 (DOI)000343215600007 ()
#####

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Available from: 2014-02-14 Created: 2014-02-14 Last updated: 2017-12-06Bibliographically approved

Open this publication in new window or tab >>High-fidelity numerical solution of the time-dependent Dirac equation### Almquist, Martin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Mattsson, Ken

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Edvinsson, Tomas

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 262, p. 86-103Article in journal (Refereed) Published
##### National Category

Computational Mathematics Theoretical Chemistry
##### Identifiers

urn:nbn:se:uu:diva-215119 (URN)10.1016/j.jcp.2013.12.038 (DOI)000330955200006 ()
#####

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Available from: 2014-01-09 Created: 2014-01-10 Last updated: 2017-12-06Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Inorganic Chemistry.

Open this publication in new window or tab >>Optimal diagonal-norm SBP operators### Mattsson, Ken

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Almquist, Martin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Carpenter, Mark H.

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##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-215785 (URN)10.1016/j.jcp.2013.12.041 (DOI)000331717100005 ()
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Available from: 2014-01-15 Created: 2014-01-16 Last updated: 2017-12-06Bibliographically approved