دانلود کتاب Mathematical Theory of Subdivision: Finite Element and Wavelet Methods

فهرست مطالب :

Preface

About the authors

1. Overview of finite element method

1. Some common governing differential equations
2. Basic steps of finite element method
3. Element stiffness matrix for a bar
4. Element stiffness matrix for single variable 2d element
5. Element stiffness matrix for a beam element
6. References for further reading

2. Wavelets

1. Wavelet basis functions
2. Wavelet-Galerkin method
3. Daubechies wavelets for boundary and initial value problems
4. References for further reading

3. Fundamentals of vector spaces

1. Introduction
2. Vector spaces
3. Normed linear spaces
4. Inner product spaces
5. Banach spaces
6. Hilbert spaces
7. Projection on finite dimensional spaces
8. Change of basis - Gram-Schmidt othogonalization process
9. Riesz bases and frame conditions
10. References for further reading

4. Operators

1. Mapping of sets, general concept of functions
2. Operators
3. Linear and adjoint operators
4. Functionals and dual space
5. Spectrum of bounded linear self-adjoint operator
6. Classification of differential operators
7. Existence, uniqueness and regularity of solution
8. References

5. Theoretical foundations of the finite element method

1. Distribution theory
2. Sobolev spaces
3. Variational Method
4. Nonconforming elements and patch test
5. References for further reading

6. Wavelet- based methods for differential equations

1. Fundamentals of continuous and discrete wavelets
2. Multiscaling
3. Classification of wavelet basis functions
4. Discrete wavelet transform
5. Lifting scheme for discrete wavelet transform
6. Lifting scheme to customize wavelets
7. Non-standard form of matrix and its solution
8. Multigrid method
9. References for further reading

7. Error - estimation

1. Introduction
2. A-priori error estimation
3. Recovery based error estimators
4. Residual based error estimators
5. Goal oriented error estimators
6. Hierarchical & wavelet based error estimator
7. References for further reading

Appendix