The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform

Jan Nordstrom - One of the best experts on this subject based on the ideXlab platform.

Eli Turkel - One of the best experts on this subject based on the ideXlab platform.

  • high order Finite Difference Methods for the helmholtz equation
    Computer Methods in Applied Mechanics and Engineering, 1998
    Co-Authors: I Singer, Eli Turkel
    Abstract:

    High-order Finite Difference Methods for solving the Helmholtz equation are developed and analyzed, in one and two dimensions on uniform grids. The standard pointwise representation has a second-order accurate local truncation error. We also study two schemes which have a fourth-order accurate local truncation error. One of the high-order schemes is based on generalizations of the Pade approximation. The second scheme is based on high-order approximation to the derivative calculated from the Helmholtz equation itself. A symmetric high-order representation is developed for a Neumann boundary condition. Numerical results are presented on model problems approximated with the developed schemes.

  • accurate Finite Difference Methods for time harmonic wave propagation
    Journal of Computational Physics, 1995
    Co-Authors: Isaac Harari, Eli Turkel
    Abstract:

    Finite Difference Methods for solving problems of time-harmonic acoustics are developed and analyzed. Multi-dimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing non-uniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or non-uniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy, and reflection, and by improving the representation of source terms. The resulting schemes have fourth order accurate local truncation error on uniform grids and third order in the non-uniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.

S B Yuste - One of the best experts on this subject based on the ideXlab platform.

  • fast accurate and robust adaptive Finite Difference Methods for fractional diffusion equations
    Numerical Algorithms, 2016
    Co-Authors: S B Yuste, Joaquin Quintanamurillo
    Abstract:

    The computation time required by standard Finite Difference Methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of the number of timesteps. Besides, the solutions of these problems usually involve markedly different time scales, which leads to quite inhomogeneous numerical errors. A natural way to address these difficulties is by resorting to adaptive numerical Methods where the size of the timesteps is chosen according to the behaviour of the solution. A key feature of these Methods is then the efficiency of the adaptive algorithm employed to dynamically set the size of every timestep. Here we discuss two adaptive Methods based on the step-doubling technique. These Methods are, in many cases, immensely faster than the corresponding standard method with fixed timesteps and they allow a tolerance level to be set for the numerical errors that turns out to be a good indicator of the actual errors.

  • weighted average Finite Difference Methods for fractional diffusion equations
    Journal of Computational Physics, 2006
    Co-Authors: S B Yuste
    Abstract:

    A class of Finite Difference Methods for solving fractional diffusion equations is considered. These Methods are an extension of the weighted average Methods for ordinary (non-fractional) diffusion equations. Their accuracy is of order (Δx)2 and Δt, except for the fractional version of the Crank-Nicholson method, where the accuracy with respect to the timestep is of order (Δt)2 if a second-order approximation to the fractional time-derivative is used. Their stability is analyzed by means of a recently proposed procedure akin to the standard von Neumann stability analysis. A simple and accurate stability criterion valid for different discretization schemes of the fractional derivative, arbitrary weight factor, and arbitrary order of the fractional derivative, is found and checked numerically. Some examples are provided in which the new Methods' numerical solutions are obtained and compared against exact solutions.

  • weighted average Finite Difference Methods for fractional diffusion equations
    arXiv: Numerical Analysis, 2004
    Co-Authors: S B Yuste
    Abstract:

    Weighted averaged Finite Difference Methods for solving fractional diffusion equations are discussed and different formulae of the discretization of the Riemann-Liouville derivative are considered. The stability analysis of the different numerical schemes is carried out by means of a procedure close to the well-known von Neumann method of ordinary diffusion equations. The stability bounds are easily found and checked in some representative examples.

Ossian Oreilly - One of the best experts on this subject based on the ideXlab platform.

Mark H Carpenter - One of the best experts on this subject based on the ideXlab platform.