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Wang, Siyang

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 >>An improved high order finite difference method for non-conforming grid interfaces for the wave equation### Wang, Siyang

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_some",{id:"formSmash:j_idt191:1:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_otherAuthors",{id:"formSmash:j_idt191:1:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 77, p. 775-792Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-320600 (URN)10.1007/s10915-018-0723-9 (DOI)000446594600004 ()
#####

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Available from: 2018-05-09 Created: 2017-04-23 Last updated: 2018-11-29Bibliographically 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 >>Convergence of finite difference methods for the wave equation in two space dimensions### Wang, Siyang

### Nissen, Anna

### Kreiss, Gunilla

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_idt191_2_j_idt195_some",{id:"formSmash:j_idt191:2:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_otherAuthors",{id:"formSmash:j_idt191:2:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 87, no 314, p. 2737-2763Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-320603 (URN)10.1090/mcom/3319 (DOI)000440340300006 ()
#####

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Available from: 2018-02-02 Created: 2017-04-23 Last updated: 2019-11-18Bibliographically 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 >>High-order numerical methods for 2D parabolic problems in single and composite domains### Ludvigsson, Gustav

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.### Steffen, Kyle R.

### Sticko, Simon

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.### Wang, Siyang

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_some",{id:"formSmash:j_idt191:3:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_some",multiple:true}); ### Xia, Qing

### Epshteyn, Yekaterina

### Kreiss, Gunilla

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_idt191_3_j_idt195_otherAuthors",{id:"formSmash:j_idt191:3:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt191_3_j_idt195_j_idt209",{id:"formSmash:j_idt191:3:j_idt195:j_idt209",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_j_idt209",onLabel:"Hide others...",offLabel:"Show others..."}); 2018 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 76, p. 812-847Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-339130 (URN)10.1007/s10915-017-0637-y (DOI)000436253800006 ()
#####

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##### Projects

eSSENCE
Available from: 2018-01-10 Created: 2018-01-16 Last updated: 2019-09-26Bibliographically approved

Open this publication in new window or tab >>An energy based discontinuous Galerkin method for acoustic–elastic waves### Appelö, Daniel

### Wang, Siyang

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_idt191_4_j_idt195_some",{id:"formSmash:j_idt191:4:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_otherAuthors",{id:"formSmash:j_idt191:4:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_otherAuthors",multiple:true}); 2017 (English)In: Proc. 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Minneapolis, MN: University of Minnesota Press, 2017, p. 389-390Conference paper, Oral presentation with published abstract (Other academic)
##### Place, publisher, year, edition, pages

Minneapolis, MN: University of Minnesota Press, 2017
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-320601 (URN)
##### Conference

WAVES 2017
#####

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Available from: 2017-05-19 Created: 2017-04-23 Last updated: 2017-06-30Bibliographically approved

Open this publication in new window or tab >>An explicit Hermite–Taylor method for the Schrödinger equation### Appelö, Daniel

### Kreiss, Gunilla

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.### Wang, Siyang

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_idt191_5_j_idt195_some",{id:"formSmash:j_idt191:5:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_5_j_idt195_otherAuthors",{id:"formSmash:j_idt191:5:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_otherAuthors",multiple:true}); 2017 (English)In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 21, p. 1207-1230Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-318850 (URN)10.4208/cicp.080815.211116a (DOI)000398841800001 ()
#####

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Available from: 2017-03-27 Created: 2017-03-29 Last updated: 2017-05-11Bibliographically approved

Open this publication in new window or tab >>Convergence of summation-by-parts finite difference methods for the wave equation### Wang, Siyang

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.### Kreiss, Gunilla

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_idt191_6_j_idt195_some",{id:"formSmash:j_idt191:6:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_otherAuthors",{id:"formSmash:j_idt191:6:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_otherAuthors",multiple:true}); 2017 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 71, p. 219-245Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-264752 (URN)10.1007/s10915-016-0297-3 (DOI)000398062500009 ()
#####

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Available from: 2016-09-27 Created: 2015-10-16 Last updated: 2017-05-17Bibliographically approved

Open this publication in new window or tab >>Finite Difference and Discontinuous Galerkin Methods for Wave Equations### Wang, Siyang

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_idt191_7_j_idt195_some",{id:"formSmash:j_idt191:7:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_otherAuthors",{id:"formSmash:j_idt191:7:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_otherAuthors",multiple:true}); 2017 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Uppsala: Acta Universitatis Upsaliensis, 2017. p. 53
##### Series

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1522
##### Keywords

Wave propagation, Finite difference method, Discontinuous Galerkin method, Stability, Accuracy, Summation by parts, Normal mode analysis
##### National Category

Computational Mathematics
##### Research subject

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

urn:nbn:se:uu:diva-320614 (URN)978-91-554-9927-3 (ISBN)
##### Public defence

2017-06-13, Room 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
##### Opponent

### Hagstrom, Thomas

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##### Supervisors

### Kreiss, Gunilla

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Available from: 2017-05-22 Created: 2017-04-23 Last updated: 2017-06-28

Wave propagation problems can be modeled by partial differential equations. In this thesis, we study wave propagation in fluids and in solids, modeled by the acoustic wave equation and the elastic wave equation, respectively. In real-world applications, waves often propagate in heterogeneous media with complex geometries, which makes it impossible to derive exact solutions to the governing equations. Alternatively, we seek approximated solutions by constructing numerical methods and implementing on modern computers. An efficient numerical method produces accurate approximations at low computational cost.

There are many choices of numerical methods for solving partial differential equations. Which method is more efficient than the others depends on the particular problem we consider. In this thesis, we study two numerical methods: the finite difference method and the discontinuous Galerkin method. The finite difference method is conceptually simple and easy to implement, but has difficulties in handling complex geometries of the computational domain. We construct high order finite difference methods for wave propagation in heterogeneous media with complex geometries. In addition, we derive error estimates to a class of finite difference operators applied to the acoustic wave equation. The discontinuous Galerkin method is flexible with complex geometries. Moreover, the discontinuous nature between elements makes the method suitable for multiphysics problems. We use an energy based discontinuous Galerkin method to solve a coupled acoustic-elastic problem.

Department of Mathematics, Southern Methodist 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 >>High order finite difference methods for the wave equation with non-conforming grid interfaces### Wang, Siyang

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.### Virta, Kristoffer

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.### Kreiss, Gunilla

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_idt191_8_j_idt195_some",{id:"formSmash:j_idt191:8:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_otherAuthors",{id:"formSmash:j_idt191:8:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_otherAuthors",multiple:true}); 2016 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 68, p. 1002-1028Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-264754 (URN)10.1007/s10915-016-0165-1 (DOI)000380693700006 ()
##### External cooperation:

#####

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Available from: 2016-01-27 Created: 2015-10-16 Last updated: 2017-12-01Bibliographically approved

Open this publication in new window or tab >>Analysis of boundary and interface closures for finite difference methods for the wave equation### Wang, Siyang

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_idt191_9_j_idt195_some",{id:"formSmash:j_idt191:9:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_9_j_idt195_otherAuthors",{id:"formSmash:j_idt191:9:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_otherAuthors",multiple:true}); 2015 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Uppsala University, 2015
##### Series

Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2015-005
##### National Category

Computational Mathematics
##### Research subject

Scientific Computing
##### Identifiers

urn:nbn:se:uu:diva-264761 (URN)
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### Kreiss, Gunilla

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Available from: 2015-10-14 Created: 2015-10-16 Last updated: 2017-08-31Bibliographically approved

We consider high order finite difference methods for the wave equations in the second order form, where the finite difference operators satisfy the summation-by-parts principle. Boundary conditions and interface conditions are imposed weakly by the simultaneous-approximation-term method, and non-conforming grid interfaces are handled by an interface operator that is based on either interpolating directly between the grids or on projecting to piecewise continuous polynomials on an intermediate grid.

Stability and accuracy are two important aspects of a numerical method. For accuracy, we prove the convergence rate of the summation-by-parts finite difference schemes for the wave equation. Our approach is based on Laplace transforming the error equation in time, and analyzing the solution to the boundary system in the Laplace space. In contrast to first order equations, we have found that the determinant condition for the second order equation is less often satisfied for a stable numerical scheme. If the determinant condition is satisfied uniformly in the right half plane, two orders are recovered from the boundary truncation error; otherwise we perform a detailed analysis of the solution to the boundary system in the Laplace space to obtain an error estimate. Numerical experiments demonstrate that our analysis gives a sharp error estimate.

For stability, we study the numerical treatment of non-conforming grid interfaces. In particular, we have explored two interface operators: the interpolation operators and projection operators applied to the wave equation. A norm-compatible condition involving the interface operator and the norm related to the SBP operator is essential to prove stability by the energy method for first order equations. In the analysis, we have found that in contrast to first order equations, besides the norm-compatibility condition an extra condition must be imposed on the interface operators to prove stability by the energy method. Furthermore, accuracy and efficiency studies are carried out for the numerical schemes.

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