Computational Framework for the Finite Element Method in MATLAB (R) and Python
portes grátis
Computational Framework for the Finite Element Method in MATLAB (R) and Python
Sumets, Pavel
Taylor & Francis Ltd
08/2022
166
Dura
Inglês
9781032209258
15 a 20 dias
390
Descrição não disponível.
1. Finite Element Method for the One-Dimensional Boundary Value Problem. 1.1 Formulation of the Problem. 1.2 Integral Equation. 1.3 Lagrange Interpolating Polynomials. 1.4 Illustrative Problem. 1.5 Algorithms of The Finite Element Method. 1.6. Quadrature Rules. 1.7. Defining Parameters of the FEM. 2. Programming One-Dimensional Finite Element Method. 2.1 Sparse Matrices in MATLAB. 2.2 Input Data Structures. 2.3 Coding Quadrature Rules. 2.4 Interpolating and Differentiating Matrices. 2.5. Calculating and Assembling Fem Matrices. 2.6 Python Implementation. 3. Finite Element Method for the Two-Dimensional Boundary Value Problem. 3.1 Model Problem. 3.2 Finite Elements Definition. 3.3. Triangulation Examples. 3.4. Linear System of the FEM. 3.5 Stiffness Matrix and Forcing Vector. 3.6. Algorithm of Solving Problem. 4. Building Two-Dimensional Meshes. 4.1. Defining Geometry. 4.2. Representing Meshes in Matrix Form for Linear Interpolation Functions. 4.3. Complementary Mesh. 4.4. Building Meshes in MATLAB. 4.5. Building Meshes in Python. 5. Programming Two-Dimensional Finite Element Method. 5.1. Assembling Global Stiffness Matrix. 5.2. Assembling Global Forcing Vector. 5.3. Calculating Local Stiffness Matrices. 5.4. Calculating Equation Coefficients. 5.5. Calculating Global Matrices. 5.6. Calculating Boundary Conditions. 5.7. Assembling Boundary Conditions 5.8. Solving Example Problem. 6. Nonlinear Basis Functions. 6.1. Linear Triangular Elements. 6.2. Curvilinear Triangular Elements. 6.3. Stiffness Matrix with Quadratic Basis. Conclusion Appendix A. Variational Formulation of a BVP. Appendix B. Discussion of Global Interpolation. Appendix C. Interpolatory Quadrature Formulas. Appendix D. Quadrature Rules and Orthogonal Polynomials. Appendix E. Computational Framework in Python.
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Computational engineering;applied mathematics;numerical methods;differential equations;boundary value;Finite element method;MATLAB;Python;mathematical analysis;Stiffness Matrix;MATLAB Code;Quadrature Rules;Interpolation Points;Python Code;Interpolation Nodes;Canonical Element;Triangular Elements;Fem System;PDE Problem;Quadratic Basis Functions;Assembling Stiffness Matrix;Finite Element Nodes;Boundary Segments;Sparse Matrix;Sparse Matrices;Quadrature Nodes;Identification Numbers;Fem Solution;NumPy Library;Complementary Mesh;Geometry Definition;Local Stiffness Matrix;Fem Framework;Mesh Points
1. Finite Element Method for the One-Dimensional Boundary Value Problem. 1.1 Formulation of the Problem. 1.2 Integral Equation. 1.3 Lagrange Interpolating Polynomials. 1.4 Illustrative Problem. 1.5 Algorithms of The Finite Element Method. 1.6. Quadrature Rules. 1.7. Defining Parameters of the FEM. 2. Programming One-Dimensional Finite Element Method. 2.1 Sparse Matrices in MATLAB. 2.2 Input Data Structures. 2.3 Coding Quadrature Rules. 2.4 Interpolating and Differentiating Matrices. 2.5. Calculating and Assembling Fem Matrices. 2.6 Python Implementation. 3. Finite Element Method for the Two-Dimensional Boundary Value Problem. 3.1 Model Problem. 3.2 Finite Elements Definition. 3.3. Triangulation Examples. 3.4. Linear System of the FEM. 3.5 Stiffness Matrix and Forcing Vector. 3.6. Algorithm of Solving Problem. 4. Building Two-Dimensional Meshes. 4.1. Defining Geometry. 4.2. Representing Meshes in Matrix Form for Linear Interpolation Functions. 4.3. Complementary Mesh. 4.4. Building Meshes in MATLAB. 4.5. Building Meshes in Python. 5. Programming Two-Dimensional Finite Element Method. 5.1. Assembling Global Stiffness Matrix. 5.2. Assembling Global Forcing Vector. 5.3. Calculating Local Stiffness Matrices. 5.4. Calculating Equation Coefficients. 5.5. Calculating Global Matrices. 5.6. Calculating Boundary Conditions. 5.7. Assembling Boundary Conditions 5.8. Solving Example Problem. 6. Nonlinear Basis Functions. 6.1. Linear Triangular Elements. 6.2. Curvilinear Triangular Elements. 6.3. Stiffness Matrix with Quadratic Basis. Conclusion Appendix A. Variational Formulation of a BVP. Appendix B. Discussion of Global Interpolation. Appendix C. Interpolatory Quadrature Formulas. Appendix D. Quadrature Rules and Orthogonal Polynomials. Appendix E. Computational Framework in Python.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Computational engineering;applied mathematics;numerical methods;differential equations;boundary value;Finite element method;MATLAB;Python;mathematical analysis;Stiffness Matrix;MATLAB Code;Quadrature Rules;Interpolation Points;Python Code;Interpolation Nodes;Canonical Element;Triangular Elements;Fem System;PDE Problem;Quadratic Basis Functions;Assembling Stiffness Matrix;Finite Element Nodes;Boundary Segments;Sparse Matrix;Sparse Matrices;Quadrature Nodes;Identification Numbers;Fem Solution;NumPy Library;Complementary Mesh;Geometry Definition;Local Stiffness Matrix;Fem Framework;Mesh Points
