On the representation of operators in bases of compactly supported wavelets
SIAM Journal on Numerical Analysis
Wavelets and the numerical solution of partial differential equations
Journal of Computational Physics
On the wavelet based differentiation matrix
Journal of Scientific Computing
Adaptive multiresolution schemes for shock computations
Journal of Computational Physics
Journal of Computational Physics
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
Solving Hyperbolic PDEs Using Interpolating Wavelets
SIAM Journal on Scientific Computing
Second-generation wavelet collocation method for the solution of partial differential equations
Journal of Computational Physics
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Hi-index | 31.45 |
Biorthogonal interpolating wavelets have been applied to electromagnetic field modeling through the wavelet collocation method in time domain, yielding a versatile first-principle algorithm for the solution of time dependent Maxwell's equations with inhomogeneous media. The resulting scheme maintains high accuracy, while, by virtue of its sub-gridding capability, significant reduction of the computational expenditure has been obtained. The proposed method has been applied to the analysis of two-dimensional dielectric waveguide discontinuities. Particularly for the modeling of electrically large optical waveguides, where the dimension of the analyzed structure is much larger than the wavelength of the highest frequency content of the transmitted signal, the proposed method has been proven to be highly efficient compared to the standard finite-difference method.