analysis and a course on partial differential equations and functional analysis or their equivalents. The students for this course should be experienced with at least one computer programming language such as C, C++ or MatLab for numerical experiments 课程教学大纲( course syllabus) After completing the course, students should be able to 1. Solve some elliptic PDEs with the finite difference method 2. Apply the fast Fourier transform method to solve finite difference equations 3. Solve some elliptic PDEs with the finite element method *学习目标 4. Apply the geometric multigrid method to solve finite element equations 5. Solve some elliptic PDEs with the boundary integral method Outcomes) 6. Solve some parabolic PDEs with the operator splitting technique 7. Solve some hyperbolic PDes with some typical TVD schemes 8. Understand the fast multipole method 9. Understand some typical Cartesian methods 10. Understand some adaptive finite element methods 教学内容 教学方式作业及要求基本要求 查方式 Credit Teaching Intended Assessment hours methodology learning methods outcomes blackboard Finite difference ng homework method for linear blackboard problems by diffusion riting plus method homework equation in 1D computer computer lectured demonstration implementation *教学内容进度| Finite difference blackboard 安排及要求 writing homework understand reaction -diffusion blackboard problems by the gradIng (Class Schedule equation and hand and method homework techniques demonstration implementation LOD and ADI riting homework understand methods for blackboard problems by equation in 2D lectured demonstration implementation Finite difference blackboard understand ng homeworkanalysis and a course on partial differential equations and functional analysis or their equivalents. The students for this course should be experienced with at least one computer programming language such as C, C++ or MatLab for numerical experiments. 课程教学大纲（course syllabus） *学习目标 (Learning Outcomes) After completing the course, students should be able to: 1．Solve some elliptic PDEs with the finite difference method 2．Apply the fast Fourier transform method to solve finite difference equations 3．Solve some elliptic PDEs with the finite element method 4．Apply the geometric multigrid method to solve finite element equations 5．Solve some elliptic PDEs with the boundary integral method 6．Solve some parabolic PDEs with the operator splitting technique 7．Solve some hyperbolic PDEs with some typical TVD schemes 8．Understand the fast multipole method 9．Understand some typical Cartesian methods 10．Understand some adaptive finite element methods *教学内容、进度 安排及要求 (Class Schedule & Requirements) 教学内容 topics 学时 Credit hours 教学方式 Teaching methodology 作业及要求 tasks 基本要求 Intended learning outcomes 考查方式 Assessment methods Finite difference method for linear diffusion equation in 1D 2 blackboard writing blackboard writing plus computer demonstration solve homework problems by hand and computer implementation understand the method lectured grading homework Finite difference for reaction-diffusion equation and operator splitting techniques 2 blackboard writing blackboard writing plus computer demonstration solve homework problems by hand and computer implementation understand the method lectured grading homework LOD and ADI methods for linear diffusion equation in 2D 2 blackboard writing blackboard writing plus computer demonstration solve homework problems by hand and computer implementation understand the method lectured grading homework Finite difference method for elliptic PDEs 3 blackboard writing blackboard solve homework problems by understand the method grading homework