Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Control of local error stabilizes integrations
Journal of Computational and Applied Mathematics
Multiresolution schemes for conservation laws with viscosity
Journal of Computational Physics
Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I
SIAM Journal on Scientific Computing
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
Journal of Parallel and Distributed Computing - Special issue on dynamic load balancing
Solving Hyperbolic PDEs Using Interpolating Wavelets
SIAM Journal on Scientific Computing
Point Value Multiscale Algorithms for 2D Compressible Flows
SIAM Journal on Scientific Computing
High Resolution Schemes for Conservation Laws with Locally Varying Time Steps
SIAM Journal on Scientific Computing
Fully adaptive multiresolution finite volume schemes for conservation laws
Mathematics of Computation
A conservative fully adaptive multiresolution algorithm for parabolic PDEs
Journal of Computational Physics
Adaptive wavelet representation and differentiation on block-structured grids
Applied Numerical Mathematics - Special issue on applied and computational mathematics: Selected papers of the fourth PanAmerican workshop
SIAM Journal on Scientific Computing
Error Estimation and Control for ODEs
Journal of Scientific Computing
Space---Time Adaptive Solution of First Order PDES
Journal of Scientific Computing
Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations
Journal of Computational Physics
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Fully Adaptive Multiscale Schemes for Conservation Laws Employing Locally Varying Time Stepping
Journal of Scientific Computing
Journal of Scientific Computing
An adaptive multiresolution scheme with local time stepping for evolutionary PDEs
Journal of Computational Physics
SIAM Journal on Scientific Computing
An adaptive multiresolution method on dyadic grids: Application to transport equations
Journal of Computational and Applied Mathematics
11 PFLOP/s simulations of cloud cavitation collapse
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Journal of Computational Physics
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Adaptive strategies in space and time allow considerable speed-up of finite volume schemes for conservation laws, while controlling the accuracy of the discretization. In this paper, a multiresolution technique for finite volume schemes with explicit time discretization is presented. An adaptive grid is introduced by suitable thresholding of the wavelet coefficients, which maintains the accuracy of the finite volume scheme of the regular grid. Further speed-up is obtained by local scale-dependent time stepping, i.e., on large scales larger time steps can be used without violating the stability condition of the explicit scheme. Furthermore, an estimation of the truncation error in time, using embedded Runge-Kutta type schemes, guarantees a control of the time step for a given precision. The accuracy and efficiency of the fully adaptive method is illustrated with applications for compressible Euler equations in one and two space dimensions.