博碩士論文 962201012 詳細資訊




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姓名 吳昭穎(Chao-Ying Wu)  查詢紙本館藏   畢業系所 數學系
論文名稱
(Numerical Simulation of Three-dimensional Blood Flows in Arteries Using Domain Decomposition Based Scientific Software Packages in Parallel Computers)
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摘要(中) 一個好的模擬工具是可根據患者特殊解剖結構和生理狀況,在臨床上被使用於幫助醫師或學者們研究血管疾病以提高診斷並且計劃手術做法。在本論文中,我們著重於開發平行區域分解演算法,為解一描述流體在血管中的方程所離散化後的非線性系統,其對空間上的離散是使用 stabilized finite element method,而時間上的離散則是使用 implicit backward Euler finite difference method。特別地,在每個 time step 是用 Newton-Krylov-Schwarz algorithm 來解這樣一個非線性系統。我們使用 PETSc 套件來實現流體模擬工具的平行化 並且將它與其他軟體合併成為一個平行化的血流模擬系統,包括 Cubit 是用來產生網格、ParMETIS 是做網格分割、而 ParaView 則作為視覺化的工具。我們利用 a straight artery model 和 an end-to-side graft model 來驗證我們平行化的程式碼正確性並且研究其演算法的平行化處理效能。
摘要(英) A good simulation tool based on patient-specific anatomy and physiological conditions can be clinically used to help physicians or researchers to study vascular diseases, to enhance diagnoses, as well as to plan surgery procedures. In this paper, we focus on developing parallel domain decomposition algorithms for solving nonlinear systems arising from the discretization of blood flow model equations, where a stabilized finite element method is used for the spatial discretization, while an implicit backward Euler finite difference method for the temporal discretization. In particular, at each time step, the resulting system solved by the Newton-Krylov-Schwarz algorithm. We implement the parallel fluid solver using PETSc and integrate it with other software packages into a parallel blood flow simulation system, including Cubit, ParMETIS and ParaView for mesh generation, mesh partitioning, and visualization, respectively. We validated our parallel code and investigated the parallel performance of our algorithms for both a straight artery model and an end-to-side graft model.
關鍵字(中) 關鍵字(英) ★ Blood flow simulation
★ Newton-Krylov-Schwarz algorithm
★ Domain decomposition
論文目次 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Background of physiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Mathematical models for blood flows in arteries . . . . . . . . . . . . . . . . 6
3.1 Nondimensionalization . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 Analytical solutions in a rigid tube . . . . . . . . . . . . . . . . . . . . . 7
3.2.1 Womersley solution . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Spatial and temporal discretizations . . . . . . . . . . . . . . . . . . . . 14
3.4 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4.1 One-level additive Schwarz preconditioners . . . . . . . . . . . . 17
4 Parallel software development . . . . . . . . . . . . . . . . . . . . . . . . . 19
5 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.1 Test cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.1.1 A long straight artery model . . . . . . . . . . . . . . . . . . . . 21
5.1.2 An end-to-side graft model . . . . . . . . . . . . . . . . . . . . . 22
5.2 Grid tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.3 Parallel code validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.3.1 A long straight artery model . . . . . . . . . . . . . . . . . . . . 26
5.3.2 An end-to-side graft model . . . . . . . . . . . . . . . . . . . . . 29
5.4 NKS algorithm parameter tuning and parallel performance study . . . . . 30
6 Conclusion and future works . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
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指導教授 黃楓南(Feng-Nan Hwang) 審核日期 2009-7-20
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