References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt151",{id:"formSmash:upper:j_idt151",widgetVar:"widget_formSmash_upper_j_idt151",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt152_j_idt154",{id:"formSmash:upper:j_idt152:j_idt154",widgetVar:"widget_formSmash_upper_j_idt152_j_idt154",target:"formSmash:upper:j_idt152:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Summation-by-parts operators for non-simply connected domainsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2016 (English)Report (Other academic)
##### Abstract [en]

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

Linköping: Linköping University Electronic Press, 2016. , 32 p.
##### Series

LiTH-MAT-R, ISSN 0348-2960 ; 2016:11
##### Keyword [en]

Initial boundary value problems, Stability, Well-posedness, Boundary conditions, Non-simply connected domains, Complex geometries
##### National Category

Computational Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-130585ISRN: LiTH-MAT-R--2016/11--SEOAI: oai:DiVA.org:liu-130585DiVA: diva2:953296
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt384",{id:"formSmash:j_idt384",widgetVar:"widget_formSmash_j_idt384",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt390",{id:"formSmash:j_idt390",widgetVar:"widget_formSmash_j_idt390",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt396",{id:"formSmash:j_idt396",widgetVar:"widget_formSmash_j_idt396",multiple:true});
Available from: 2016-08-17 Created: 2016-08-17 Last updated: 2016-08-31Bibliographically approved
##### In thesis

We construct fully discrete stable and accurate numerical schemes for solving partial differential equations posed on non-simply connected spatial domains. The schemes are constructed using summation-by-parts operators in combination with a weak imposition of initial and boundary conditions using the simultaneous approximation term technique.

In the theoretical part, we consider the two dimensional constant coefficient advection equation posed on a rectangular spatial domain with a hole. We construct the new scheme and study well-posedness and stability. Once the theoretical development is done, the technique is extended to more complex non-simply connected geometries.

Numerical experiments corroborate the theoretical results and show the applicability of the new approach and its advantages over the standard multi-block technique. Finally, an application using the linearized Euler equations for sound propagation is presented.

1. Stable High Order Finite Difference Methods for Wave Propagation and Flow Problems on Deforming Domains$(function(){PrimeFaces.cw("OverlayPanel","overlay956877",{id:"formSmash:j_idt663:0:j_idt667",widgetVar:"overlay956877",target:"formSmash:j_idt663:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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