Applied Numerical Mathematics 61 (January 2011)

IFC_[first_author]_2011_Applied-Numerical-Mathematics......Page 1
Introduction......Page 2
Mathematical formulation of MHD equations......Page 4
Methodology fundamentals......Page 6
Rectangular mesh......Page 7
Triangular mesh......Page 10
Time discretization......Page 11
Case studies......Page 16
Problem 1: duct with insulating walls, λ=infty and horizontal magnetic field, θ=0......Page 17
Problem 3: duct under oblique magnetic field, θ>0......Page 20
Problem 4: duct with M=0, λ,θ=arbitrary......Page 21
References......Page 22
Introduction......Page 25
Stochastic collocation methods......Page 26
Integration for high-dimensional problems......Page 27
Gauss-Patterson quadrature rules......Page 29
Error estimation and adaptivity in the sparse grid construction......Page 30
Applications to electromagnetic scattering problems......Page 32
Nodal discontinuous Galerkin finite element method......Page 33
Low-dimensional examples......Page 34
Example of a higher-dimensional problem......Page 36
Acknowledgement......Page 37
References......Page 38
Introduction......Page 39
Numerov's method......Page 40
Linear monotone iterative algorithm......Page 43
Convergence of the method......Page 46
Applications and numerical results......Page 47
Concluding remarks......Page 51
References......Page 52
Introduction......Page 54
The governing equations......Page 55
Optimal control problem......Page 56
Newton's method......Page 57
Space discretization of dual problem......Page 58
Spatial grid adaptivity......Page 59
Parameters used in the simulation......Page 60
Test case 1......Page 61
Test case 2......Page 64
Conclusions......Page 65
References......Page 66
Introduction......Page 67
Dimensional splitting......Page 68
Convergence of the fixed-point iteration......Page 69
Implementation aspects......Page 72
Steady problems......Page 73
Choosing α......Page 75
Conclusions and future work......Page 76
References......Page 77
Introduction......Page 78
Radial basis function approximation......Page 79
1D iterative adaptive RBF methods......Page 80
Iterative adaptive RBF method for 2D edges......Page 81
2D global extension method......Page 82
Ill-conditioning and rescaling domain intervals......Page 83
1D domain decomposition methods......Page 84
Global extension method......Page 85
Dimension by dimension method......Page 87
Conclusions......Page 89
References......Page 92
Introduction......Page 93
First method......Page 94
Regularization method......Page 95
Approximation by the finite element method......Page 101
Numerical examples......Page 104
References......Page 108
Introduction......Page 109
Optimize compact finite difference stencils......Page 111
Quantifying the spatial resolution......Page 112
Non-periodic boundary and near boundary stencils......Page 113
Spatial resolution properties......Page 115
Boundary stencil......Page 116
Evaluating the free parameters......Page 117
Numerical stability of optimized composite templates......Page 120
Applications of optimized composite templates......Page 123
Non-linear viscous burgers equation......Page 124
Two-dimensional acoustic scattering......Page 128
References......Page 130
Introduction......Page 132
IAEs of index-2......Page 134
The Jacobi collocation scheme......Page 137
Convergence analysis......Page 140
Numerical results and discussions......Page 145
Conclusion......Page 148
References......Page 149