Numerical solution methods

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Table of contents

Introduction 
1 State of the art in inverse problems. The problem of deconvolution 
1.1 Discrete convolution and deconvolution. Properties of the Toeplitz matrix
1.2 Numerical solution methods
1.3 Numerical methods for Toeplitz matrices
2 Monitoring of displacements 
2.1 Structural dynamics
2.1.1 Model problem
2.1.2 Time integration methods
2.1.3 Modal method
2.1.4 Harmonic Analysis
2.1.5 Example
2.2 Model order reduction techniques
2.2.1 Proper orthogonal decomposition
2.2.2 Reduced Basis Method
2.2.3 Proper Generalized Decomposition
2.3 Generalized transfer function
2.4 Generalized impulse response
2.5 Generalized displacements
2.5.1 Generalized displacements in frequency space
2.5.2 Generalized displacements in time domain
2.6 Results
2.7 Fractional damping
2.7.1 Fractional damping as a parameter
2.7.2 Results
3 Monitoring of forces 
3.1 Formulation of the problem
3.2 Generalized inverse impulse response
3.2.1 Dual problem. Flexibility method
3.2.2 Training
3.2.3 Avoiding regularization with the separated representation
3.2.4 Computation of the generalized inverse impulse response
3.3 Results
4 Nonlinear applications of the Generalized Impulse Response
4.1 Generalized impulse response application in nonlinear problems
4.2 Nonlinear external applied force
4.3 Nonlinear stiffness
4.4 Numerical examples
4.4.1 Nonlinear external applied force
4.4.2 Nonlinear stiffness
Conclusions 
Bibliography 
Appendix