Local Factorization of Multidimensional Differential Operators to Optimize Implicit Solution Methods

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dc.contributor.advisorLamoureux, Michael P.
dc.contributor.authorVestrum, Robert J.
dc.contributor.committeememberTrad, Daniel Osvaldo
dc.contributor.committeememberLiao, Wenyuan
dc.date2021-06
dc.date.accessioned2021-05-17T17:45:14Z
dc.date.available2021-05-17T17:45:14Z
dc.date.issued2021-05-14
dc.description.abstractSolving multidimensional differential operators using implicit finite-difference methods involves a computationally intensive step of calculating the solution to a system that involves both the current and future state of the system. If a linear operator can be expressed as an affine combination of sufficiently many orthogonal finite-difference approximations, then it is possible to factor the operator as product of an upper triangular matrix and that matrix's adjoint. Using the factor calculated in this Affine Local Grid Factorization (ALG-F), it is possible to solve the system by simple back substitution followed by forward substitution resulting in an implicit scheme that is O(N) rather than O(N^2) typical in implicit finite-difference schemes. Included are the equations to calculate the ALG Factorization for the wave equation in two and three dimensions to demonstrate the method provides robust and accurate results.en_US
dc.identifier.citationVestrum, R. J. (2021). Local Factorization of Multidimensional Differential Operators to Optimize Implicit Solution Methods (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/38874
dc.identifier.urihttp://hdl.handle.net/1880/113427
dc.language.isoengen_US
dc.publisher.facultyScienceen_US
dc.publisher.institutionUniversity of Calgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.en_US
dc.subjectHyperbolic PDEen_US
dc.subjectPartial Differential Equationen_US
dc.subjectImplicit Finite Difference Methoden_US
dc.subjectLocal Griden_US
dc.subjectBack-Substitutionen_US
dc.subjectFinite-Difference Methoden_US
dc.subjectFactorizationen_US
dc.subjectLaplace Operatoren_US
dc.subject.classificationEducation--Mathematicsen_US
dc.titleLocal Factorization of Multidimensional Differential Operators to Optimize Implicit Solution Methodsen_US
dc.typemaster thesisen_US
thesis.degree.disciplineMathematics & Statisticsen_US
thesis.degree.grantorUniversity of Calgaryen_US
thesis.degree.nameMaster of Science (MSc)en_US
ucalgary.item.requestcopytrueen_US
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