Spectral and finite difference solutions of the Burgers equation
Computers and Fluids
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Krylov methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
A posteriori error estimation and adaptive mesh-refinement techniques
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
Journal of Computational Physics
Wavelet solutions for the Dirichlet problem
Numerische Mathematik
Adaptive multiresolution collocation methods for initial boundary value problems of nonlinear PDEs
SIAM Journal on Numerical Analysis
A posteriori error estimates for elliptic problems in two and three space dimensions
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Stable multiscale bases and local error estimation for elliptic problems
Applied Numerical Mathematics - Special issue on multilevel methods
An adaptive wavelet-vaguelette algorithm for the solution of PDEs
Journal of Computational Physics
A fast algorithm for particle simulations
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases
Journal of Computational Physics
A fast adaptive wavelet collocation algorithm for multidimensional PDEs
Journal of Computational Physics
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
A Wavelet-Optimized, Very High Order Adaptive Grid and Order Numerical Method
SIAM Journal on Scientific Computing
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
Solving Hyperbolic PDEs Using Interpolating Wavelets
SIAM Journal on Scientific Computing
A multigrid algorithm for nonlocal collisional electrostatic drift-wave turbulence
Journal of Computational Physics
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Phase Space Error Control for Dynamical Systems
SIAM Journal on Scientific Computing
Second-generation wavelet collocation method for the solution of partial differential equations
Journal of Computational Physics
Adaptive wavelet methods for elliptic operator equations: convergence rates
Mathematics of Computation
Adaptive Wavelet Schemes for Elliptic Problems---Implementation and Numerical Experiments
SIAM Journal on Scientific Computing
A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
THE NONLINEAR GALERKIN METHOD: A MULTI-SCALE METHOD APPLIED TO THE SIMULATION OF HOMOGENEOUS TURBULENT FLOWS
An adaptive multilevel wavelet collocation method for elliptic problems
Journal of Computational Physics
An adaptive multiresolution scheme with local time stepping for evolutionary PDEs
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
Simulating 2D Waves Propagation in Elastic Solid Media Using Wavelet Based Adaptive Method
Journal of Scientific Computing
A wavelet-based multiresolution approach to large-eddy simulation of turbulence
Journal of Computational Physics
Wavelet-based method for stability analysis of vibration control systems with multiple delays
Computational Mechanics
SIAM Journal on Scientific Computing
SIAM Journal on Control and Optimization
Hi-index | 31.46 |
Dynamically adaptive numerical methods have been developed to efficiently solve differential equations whose solutions are intermittent in both space and time. These methods combine an adjustable time step with a spatial grid that adapts to spatial intermittency at a fixed time. The same time step is used for all spatial locations and all scales: this approach clearly does not fully exploit space-time intermittency. We propose an adaptive wavelet collocation method for solving highly intermittent problems (e.g. turbulence) on a simultaneous space-time computational domain which naturally adapts both the space and time resolution to match the solution. Besides generating a near optimal grid for the full space-time solution, this approach also allows the global time integration error to be controlled. The efficiency and accuracy of the method is demonstrated by applying it to several highly intermittent (1D+t)-dimensional and (2D+t)-dimensional test problems. In particular, we found that the space-time method uses roughly 18 times fewer space-time grid points and is roughly 4 times faster than a dynamically adaptive explicit time marching method, while achieving similar global accuracy.