Absorbing boundaries for wave propagation problems
Journal of Computational Physics
A variational formulation for the Chebyshev pseudospectral approximation of Neumann problems
SIAM Journal on Numerical Analysis
Effective numerical algorithms for the solution of algebraic systems arising in spectral methods
Applied Numerical Mathematics
Pole condition for singular problems: the pseudospectral approximation
Journal of Computational Physics
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates
Journal of Computational Physics
Journal of Computational Physics
A conservative staggered-grid Chebyshev multidomain method for compressible flows
Journal of Computational Physics
SIAM Journal on Scientific Computing
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Finite-element solution of nonlinear time-dependent exterior wave problems
Journal of Computational Physics
Numerical treatment of polar coordinate singularities
Journal of Computational Physics
Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations
Applied Numerical Mathematics
Dispersion Analysis for Discontinuous Spectral Element Methods
Journal of Scientific Computing
Global discrete artificial boundary conditions for time-dependent wave propagation
Journal of Computational Physics
Journal of Computational Physics
Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems
Mathematics of Computation
A multi-domain Fourier pseudospectral time-domain method for the linearized Euler equations
Journal of Computational Physics
Hi-index | 31.45 |
A multidomain Legendre pseudospectral method is developed for the solution of linear hyperbolic initial boundary value problems, with mixed boundary conditions, in general two-dimensional and axisymmetric geometries. A weak collocation spectral method is utilized for the spatial approximation of a generic wave evolution equation over multiple nonoverlapping subdomains. The system of ordinary differential equations that stems from the above procedure is integrated in time by implicit as well as explicit high order temporal approximation algorithms. The weak formalism of the influence matrix method is combined with the implicit approximation, so as to efficiently solve the coupled system of linear equations after the full discretization, while a novel technique for avoiding the amplification of roundoff error at high temporal resolution simulations with the implicit temporal integration methods, is also studied. An innovative method for the treatment of Dirichlet boundary conditions is proposed, in order to avoid the order reduction which usually arises with the utilization of the explicit time integrator. Furthermore, appropriate modifications are reported, for dealing with the pole singularity problem faced by the weak formulation of axisymmetric problems. Finally, numerical simulations of a variety of wave problems on curvilinear geometries and unstructured subdomain configurations are presented in order to assess the capabilities of the proposed methodology in handling efficiently general hyperbolic differential operators.