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課程名稱 |
科學計算一
SCIENTIFIC COMPUTING(I) |
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開課學期 |
98-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
王偉仲 |
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課號 |
MATH7411 |
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課程識別碼 |
221 U3640 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期三2,3,4(9:10~12:10) |
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上課地點 |
新405 |
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備註 |
上機教室：計中212。
總人數上限：50人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/981sc |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Finite Element Computations with Mefisto and Programming of Finite Element Softwares |
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課程目標 |
- To solve classical problems by the using of finite element softwares
- To obtain numerical results and analyze its
- To penetrate sofwares to discover the data structures and algorithms
- To program an extension of a software |
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課程要求 |
- The simplest example: 1D finite element approximation of the steady heat transfer problem
. Theory and Algorithms
. Program to do
- Short course on Fortran 77, C++ and HTML
- The presentation of the Mefisto software options with examples and exercises:
. What Mefisto can solve
. How to install it
. The initialization: INITIER
. The 1D 2D 3D mesher: MAILLER
. The Object creation: MAILLER
. The data structures of a mesh: xyzsommet+nsef, xyznoeud+topologie+npef
. The steady or unsteady heat transfer problem: THERMICER
. The eigenvalues and eigenvectors of the -div A grad operator: THERMICER
. The wave equation: THERMICER
. The steady or dynamic elasticity: ELASTICER
. The elastic eigenmodes: ELASTICER
. The steady or unsteady flow of incompressible Stokes fluids: FLUIDER
- A methodology to pass from Partial Differential Equations of a problem to the computer program
- Application to the solution of the steady heat transfer problem by the isoparametric
finite element using Lagrange polynomials interpolation:
. Partial Differential Equations and boundary conditions
. Variational Formulation
. Reference finite element with its Lagrange polynomials
. Isoparametric finite element approximation
. Approximation on the boundary
. Quadrature formula
. Elementary matrix and vector
. Global matrix and vector
. Algorithms to take in account the Dirichlet boundary condition
. Heat flux
. Operators and Operands
. Algorithm from operators and operands
. Algorithms to assemble and solve the linear system
. Programming with a computer language:
* C++ program Laplace3d.cpp to solve the Laplace problem with P1 tetrahedra
* Fortran 77 program ppther.f of Mefisto
- Choice of a project to write with fortran 77 or c++ or PETSc or SLEPc and its integration into Mefisto
- Algorithm to solve the unsteady heat transfer problem
- Algorithm to solve the wave equation
- Algorithm to find the eigenvalues and eigenvectors of the -div A grad operator
- Algorithm to solve the steady and unsteady elasticity problem
- Algorithm to find the eigenmodes and eigenvectors of the elasticity operator
- Algorithm to solve the steady and unsteady thermo-elasticity problem
- Algorithm to solve the steady or unsteady flow of incompressible Stokes fluids
with triangle or tetrahedron Taylor-Hood or Brezzi-Fortin finite elements
- Mefisto algorithms to construct the mesh of points, lines, surfaces and volumes
- Mefisto algorithm to create the mesh of an object
- Mefisto algorithms to visualize the solution
- Mefisto menus, documentation, language and data management
- Mefisto memory management
Students' work:
- Fortran 77 or C++ program of the 1d case of the steady heat transfer problem
- Choice and Mefisto solution of an heat transfer problem
- Choice and Mefisto solution of an elasticity problem
- Choice and Mefisto solution of an incompressible Stokes fluid problem
- Choice and f77 or C++ or PETSc or SLEPc programming of a project and integration into Mefisto
- Construction of a web personal page on the TIMS web server to report
all solved problems with presentation, meshes, programs, program data,
solution drawings, comments, user's manual, video, comparaisons and conclusions. |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
To be announced in the classes. |
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參考書目 |
To be announced in the classes. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
口語報告 |
20% |
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2. |
小組計畫 |
40% |
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3. |
個人計畫 |
30% |
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4. |
上課表現 |
10% |
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