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Fast, High-order Algorithms for Simulating Vesicle Flows Through Periodic Geometries.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Fast, High-order Algorithms for Simulating Vesicle Flows Through Periodic Geometries./
Author:	Marple, Gary Ray.
Description:	1 online resource (126 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.
Contained By:	Dissertation Abstracts International78-07B(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369588903

Fast, High-order Algorithms for Simulating Vesicle Flows Through Periodic Geometries.
Marple, Gary Ray.

Fast, High-order Algorithms for Simulating Vesicle Flows Through Periodic Geometries. - 1 online resource (126 pages)

Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

This dissertation presents a new boundary integral equation (BIE) method for simulating vesicle flows through periodic geometries. We begin by describing the periodization scheme, in the absence of vesicles, for singly and doubly periodic geometries in 2 dimensions and triply periodic geometries in three dimensions. Later, the periodization scheme will be expanded to include multiple vesicles confined by singly periodic channels of arbitrary shape. Rather than relying on the periodic Green's function as classical BIE methods do, the method combines the free-space Green's function with a small auxiliary basis and imposes periodicity as an extra linear condition. As a result, we can exploit existing free-space solver libraries, quadratures, and fast algorithms to handle a large number of vesicles in a geometrically complex domain. Spectral accuracy in space is achieved using the periodic trapezoid rule and product quadratures, while a first-order semi-implicit scheme evolves particles by treating the vesicle-channel interactions explicitly. New constraint-correction formulas are introduced that preserve reduced areas of vesicles, independent of the number of time steps taken. By using two types of fast algorithms, (i) the fast multipole method (FMM) for the computation of the vesicle-vesicle and the vesicle-channel hydrodynamic interaction, and (ii) a fast direct solver for the BIE on the fixed channel geometry, the computational cost is reduced to O(N) per time step where N is the spatial discretization size. We include two example applications that utilize BIE methods with periodic boundary conditions. The first seeks to determine the equilibrium shapes of periodic planar elastic membranes. The second models the opening and closing of mechanosensitive (MS) channels on the membrane of a vesicle when exposed to shear stress while passing through a constricting channel.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369588903Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Fast, High-order Algorithms for Simulating Vesicle Flows Through Periodic Geometries.
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245 1 0 $a Fast, High-order Algorithms for Simulating Vesicle Flows Through Periodic Geometries.
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500 $a Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.
500 $a Advisers: Lola Eniola-Adefeso; Shravan Kumar Veerapaneni.
502 $a Thesis (Ph.D.) $c University of Michigan $d 2016.
504 $a Includes bibliographical references
520 $a This dissertation presents a new boundary integral equation (BIE) method for simulating vesicle flows through periodic geometries. We begin by describing the periodization scheme, in the absence of vesicles, for singly and doubly periodic geometries in 2 dimensions and triply periodic geometries in three dimensions. Later, the periodization scheme will be expanded to include multiple vesicles confined by singly periodic channels of arbitrary shape. Rather than relying on the periodic Green's function as classical BIE methods do, the method combines the free-space Green's function with a small auxiliary basis and imposes periodicity as an extra linear condition. As a result, we can exploit existing free-space solver libraries, quadratures, and fast algorithms to handle a large number of vesicles in a geometrically complex domain. Spectral accuracy in space is achieved using the periodic trapezoid rule and product quadratures, while a first-order semi-implicit scheme evolves particles by treating the vesicle-channel interactions explicitly. New constraint-correction formulas are introduced that preserve reduced areas of vesicles, independent of the number of time steps taken. By using two types of fast algorithms, (i) the fast multipole method (FMM) for the computation of the vesicle-vesicle and the vesicle-channel hydrodynamic interaction, and (ii) a fast direct solver for the BIE on the fixed channel geometry, the computational cost is reduced to O(N) per time step where N is the spatial discretization size. We include two example applications that utilize BIE methods with periodic boundary conditions. The first seeks to determine the equilibrium shapes of periodic planar elastic membranes. The second models the opening and closing of mechanosensitive (MS) channels on the membrane of a vesicle when exposed to shear stress while passing through a constricting channel.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Michigan. $b Applied and Interdisciplinary Mathematics. $3 1180800
773 0 $t Dissertation Abstracts International $g 78-07B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10391680 $z click for full text (PQDT)