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Fast, High-order Algorithms for Simu...
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Marple, Gary Ray.
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Fast, High-order Algorithms for Simulating Vesicle Flows Through Periodic Geometries.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Fast, High-order Algorithms for Simulating Vesicle Flows Through Periodic Geometries./
作者:
Marple, Gary Ray.
出版者:
Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:
126 p.
附註:
Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.
Contained By:
Dissertation Abstracts International78-07B(E).
標題:
Applied mathematics. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10391680
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.
- Ann Arbor : ProQuest Dissertations & Theses, 2016 - 126 p.
Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.
Thesis (Ph.D.)--University of Michigan, 2016.
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.
ISBN: 9781369588903Subjects--Topical Terms:
2122814
Applied mathematics.
Fast, High-order Algorithms for Simulating Vesicle Flows Through Periodic Geometries.
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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.
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