Discrete exterior calculus and exact controllability for time-harmonic acoustic wave simulation

Diskreetti ulkoinen laskenta (engl, discrete exterior calculus, DEC) on differentiaaliyhtälöiden ratkaisemiseen soveltuva diskretointimenetelmä, joka säilyttää tiettyjä fysikaalisten mallien geometrisia ominaisuuksia ja tuottaa laskennallisesti tehokkaita algoritmeja. Tutkielmassa tarkastellaan kein...

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Main Author: Myyrä, Mikael
Other Authors: Informaatioteknologian tiedekunta, Faculty of Information Technology, Informaatioteknologia, Information Technology, Jyväskylän yliopisto, University of Jyväskylä
Format: Master's thesis
Language:eng
Published: 2023
Subjects:
Online Access: https://jyx.jyu.fi/handle/123456789/89358
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author Myyrä, Mikael
author2 Informaatioteknologian tiedekunta Faculty of Information Technology Informaatioteknologia Information Technology Jyväskylän yliopisto University of Jyväskylä
author_facet Myyrä, Mikael Informaatioteknologian tiedekunta Faculty of Information Technology Informaatioteknologia Information Technology Jyväskylän yliopisto University of Jyväskylä Myyrä, Mikael Informaatioteknologian tiedekunta Faculty of Information Technology Informaatioteknologia Information Technology Jyväskylän yliopisto University of Jyväskylä
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description Diskreetti ulkoinen laskenta (engl, discrete exterior calculus, DEC) on differentiaaliyhtälöiden ratkaisemiseen soveltuva diskretointimenetelmä, joka säilyttää tiettyjä fysikaalisten mallien geometrisia ominaisuuksia ja tuottaa laskennallisesti tehokkaita algoritmeja. Tutkielmassa tarkastellaan keinoja tehostaa DEC:n suorituskykyä aikaharmonisten ratkaisujen selvittämisessä akustisten aaltojen sirontaa kuvaaville tehtäville. Tähän käytetään harmonisille malleille suunniteltuja operaattoreita ja eksaktiin kontrolloitavuuteen perustuvaa optimointimenetelmää. Toteutetuissa kokeiluissa harmoniset operaattorit lisäävät menetelmän tarkkuutta huomattavasti, kun taas kontrollimenetelmä osoittautuu hyväksi valinnaksi vain tehtävissä, joiden geometria on huomattavan epäkonveksia. Laskentaverkon laadulla on suuri merkitys tutkittujen menetelmien tarkkuudessa ja stabiilisuudessa. Discrete exterior calculus (DEC) is a discretization method for differential equations which preserves important geometric properties of physical models and produces computationally efficient algorithms. We investigate ways to improve the performance of DEC in the context of time-periodic solutions to acoustic wave scattering problems by using operators purpose-built for harmonic problems and an optimization approach based on exact controllability. The harmonic operators are found to improve accuracy significantly, while the controllability method is found to be a good choice only in problems with highly nonconvex geometry. Computation mesh quality is identified as a key issue in the accuracy and stability of these methods.
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spellingShingle Myyrä, Mikael Discrete exterior calculus and exact controllability for time-harmonic acoustic wave simulation discrete exterior calculus exact controllability time-harmonic Tietotekniikka Mathematical Information Technology 602 akustiikka numeeriset menetelmät simulointi osittaisdifferentiaaliyhtälöt acoustics (phonics) numerical methods simulation partial differential equations
title Discrete exterior calculus and exact controllability for time-harmonic acoustic wave simulation
title_full Discrete exterior calculus and exact controllability for time-harmonic acoustic wave simulation
title_fullStr Discrete exterior calculus and exact controllability for time-harmonic acoustic wave simulation Discrete exterior calculus and exact controllability for time-harmonic acoustic wave simulation
title_full_unstemmed Discrete exterior calculus and exact controllability for time-harmonic acoustic wave simulation Discrete exterior calculus and exact controllability for time-harmonic acoustic wave simulation
title_short Discrete exterior calculus and exact controllability for time-harmonic acoustic wave simulation
title_sort discrete exterior calculus and exact controllability for time harmonic acoustic wave simulation
title_txtP Discrete exterior calculus and exact controllability for time-harmonic acoustic wave simulation
topic discrete exterior calculus exact controllability time-harmonic Tietotekniikka Mathematical Information Technology 602 akustiikka numeeriset menetelmät simulointi osittaisdifferentiaaliyhtälöt acoustics (phonics) numerical methods simulation partial differential equations
topic_facet 602 Mathematical Information Technology Tietotekniikka acoustics (phonics) akustiikka discrete exterior calculus exact controllability numeeriset menetelmät numerical methods osittaisdifferentiaaliyhtälöt partial differential equations simulation simulointi time-harmonic
url https://jyx.jyu.fi/handle/123456789/89358 http://www.urn.fi/URN:NBN:fi:jyu-202310035379
work_keys_str_mv AT myyrämikael discreteexteriorcalculusandexactcontrollabilityfortimeharmonicacousticwavesimulation