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You searched for subject:(quadrature by expansion). Showing records 1 – 2 of 2 total matches.

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1. Wala, Mateusz Michal. High-order numerical methods for layer potential evaluation.

Degree: PhD, Computer Science, 2019, University of Illinois – Urbana-Champaign

This thesis addresses a number of obstacles in the practical realization of integral equation methods for boundary value problems of elliptic partial differential equations. Layer potentials play a central role in the integral equation formulation of boundary value problems. However, the numerical evaluation of layer potentials presents significant practical challenges associated with issues of singular/near-singular quadrature and efficient scaling. Quadrature by Expansion (QBX) is a quadrature method that addresses many of the issues encountered in the evaluation of layer potentials, by providing a high-order and kernel/dimension independent quadrature scheme that is also acceleration-compatible, i.e., able to be integrated with a fast summation scheme to reduce the cost of O(N2) pairwise interactions to O(N). The focus of the first part of this thesis is an acceleration scheme for QBX based on the Fast Multipole Method (FMM) that provides both high performance and strong accuracy guarantees for mathematical control over the error introduced by acceleration. The scheme extends to both two and three dimensions and Laplace and Helmholtz kernels. The contribution in this thesis also includes a geometry processing framework to prepare arbitrary smooth geometries for accurate quadrature with QBX, a comprehensive complexity and error analysis of the algorithm, and a cost model and study of key optimizations. This thesis also considers the application of layer potentials to the problem of numerical conformal mapping. It is shown how there is a strong connection between the double-layer potential and the Faber/Faber-Laurent polynomials, which are polynomials closely related to the series expansion of the Riemann map. From this, a scheme for computing the Riemann map of a piecewise smooth Jordan domain is devised. This latter work also provides an insight into the convergence behavior of QBX. Finally, this thesis describes a software abstraction for the design and implementation of time integration algorithms for the solution of initial value problems. This abstraction, Dagrt, has two aims. The first is a epresentation that decouples the mathematical specification of a time integration algorithm from its realization in a particular programming model, and the second is to give the user control over implementation details. We demonstrate the capabilities of this abstraction by presenting Leap, a collection of pre-written time integration algorithm specifications that includes complex multistep and multistage methods. Advisors/Committee Members: Klöckner, Andreas (advisor), Klöckner, Andreas (Committee Chair), Olson, Luke (committee member), Fischer, Paul (committee member), Greengard, Leslie (committee member).

Subjects/Keywords: integral equations; layer potentials; fast multipole method; singular integrals; quadrature by expansion; conformal mapping; time integration

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Wala, M. M. (2019). High-order numerical methods for layer potential evaluation. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/106232

Chicago Manual of Style (16th Edition):

Wala, Mateusz Michal. “High-order numerical methods for layer potential evaluation.” 2019. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed May 07, 2021. http://hdl.handle.net/2142/106232.

MLA Handbook (7th Edition):

Wala, Mateusz Michal. “High-order numerical methods for layer potential evaluation.” 2019. Web. 07 May 2021.

Vancouver:

Wala MM. High-order numerical methods for layer potential evaluation. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2019. [cited 2021 May 07]. Available from: http://hdl.handle.net/2142/106232.

Council of Science Editors:

Wala MM. High-order numerical methods for layer potential evaluation. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2019. Available from: http://hdl.handle.net/2142/106232


KTH

2. Bagge, Joar. Numerical simulation of an inertial spheroidal particle in Stokes flow.

Degree: NA, 2015, KTH

Particle suspensions occur in many situations in nature and industry. In this master’s thesis, the motion of a single rigid spheroidal particle immersed in Stokes flow is studied numerically using a boundary integral method and a new specialized quadrature method known as quadrature by expansion (QBX). This method allows the spheroid to be massless or inertial, and placed in any kind of underlying Stokesian flow.   A parameter study of the QBX method is presented, together with validation cases for spheroids in linear shear flow and quadratic flow. The QBX method is able to compute the force and torque on the spheroid as well as the resulting rigid body motion with small errors in a short time, typically less than one second per time step on a regular desktop computer. Novel results are presented for the motion of an inertial spheroid in quadratic flow, where in contrast to linear shear flow the shear rate is not constant. It is found that particle inertia induces a translational drift towards regions in the fluid with higher shear rate.

Partikelsuspensioner förekommer i många sammanhang i naturen och industrin. I denna masteruppsats studeras rörelsen hos en enstaka stel sfäroidisk partikel i Stokesflöde numeriskt med hjälp av en randintegralmetod och en ny specialiserad kvadraturmetod som kallas quadrature by expansion (QBX). Metoden fungerar för masslösa eller tröga sfäroider, som kan placeras i ett godtyckligt underliggande Stokesflöde.   En parameterstudie av QBX-metoden presenteras, tillsammans med valideringsfall för sfäroider i linjärt skjuvflöde och kvadratiskt flöde. QBX-metoden kan beräkna kraften och momentet på sfäroiden samt den resulterande stelkroppsrörelsen med små fel på kort tid, typiskt mindre än en sekund per tidssteg på en vanlig persondator. Nya resultat presenteras för rörelsen hos en trög sfäroid i kvadratiskt flöde, där skjuvningen till skillnad från linjärt skjuvflöde inte är konstant. Det visar sig att partikeltröghet medför en drift i sidled mot områden i fluiden med högre skjuvning.

Subjects/Keywords: Fluid mechanics; Stokes flow; rigid body dynamics; spheroidal particles; inertia; integral equations; boundary integrals; double layer potentials; quadrature by expansion; Jeffery orbits; linear shear flow; quadratic flow; paraboloidal flow; Strömningsmekanik; Stokesflöde; stelkroppsdynamik; sfäroidiska partiklar; tröghet; integralekvationer; randintegraler; dubbellagerpotentialer; quadrature by expansion; Jeffery-banor; linjärt skjuvflöde; kvadratiskt flöde; paraboloidiskt flöde

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Bagge, J. (2015). Numerical simulation of an inertial spheroidal particle in Stokes flow. (Thesis). KTH. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-180290

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Bagge, Joar. “Numerical simulation of an inertial spheroidal particle in Stokes flow.” 2015. Thesis, KTH. Accessed May 07, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-180290.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Bagge, Joar. “Numerical simulation of an inertial spheroidal particle in Stokes flow.” 2015. Web. 07 May 2021.

Vancouver:

Bagge J. Numerical simulation of an inertial spheroidal particle in Stokes flow. [Internet] [Thesis]. KTH; 2015. [cited 2021 May 07]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-180290.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bagge J. Numerical simulation of an inertial spheroidal particle in Stokes flow. [Thesis]. KTH; 2015. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-180290

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.