On a wavelet-based method for the numerical simulation of wave propagation
Journal of Computational Physics
Fast visualization of volume emissions using conservative subdivision
Mathematics and Computers in Simulation
An adaptive multilevel wavelet collocation method for elliptic problems
Journal of Computational Physics
Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations
Journal of Computational Physics
Adaptive multiresolution WENO schemes for multi-species kinematic flow models
Journal of Computational Physics
A modified wavelet approximation of deflections for solving PDEs of beams and square thin plates
Finite Elements in Analysis and Design
Multiscale cell-based coarsening for discontinuous problems
Mathematics and Computers in Simulation
ENO adaptive method for solving one-dimensional conservation laws
Applied Numerical Mathematics
Simulating 2D Waves Propagation in Elastic Solid Media Using Wavelet Based Adaptive Method
Journal of Scientific Computing
Grid structure impact in sparse point representation of derivatives
Journal of Computational and Applied Mathematics
Wavelet-based signal analysis of a vehicle crash test with a fixed safety barrier
ECC'10 Proceedings of the 4th conference on European computing conference
Wavelet-based signal analysis of a vehicle crash test
WSEAS Transactions on Signal Processing
Journal of Computational Electronics
Multiscale modelling of bubbly systems using wavelet-based mesh adaptation
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
Adaptive wavelet collocation methods for image segmentation using TV---Allen---Cahn type models
Advances in Computational Mathematics
11 PFLOP/s simulations of cloud cavitation collapse
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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A method is presented for adaptively solving hyperbolic PDEs. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. The adaptability is performed automatically by thresholding the wavelet coefficients. Operations such as differentiation and multiplication are fast and simple due to the one-to-one correspondence between point values and wavelet coefficients in the interpolating basis. Treatment of boundary conditions is simplified in this sparse point representation (SPR). Numerical examples are presented for one- and two-dimensional problems. It is found that the proposed method outperforms a finite difference method on a uniform grid for certain problems in terms of flops.