∫∫ −=⎟⎟⎠⎞⎜⎜⎝⎛∂=∂ )()()( dkekikFdkekFxf Computational seismology – Pseudospectral methods

However, the space derivatives are calculated using orthogonal functions (e.g. Fourier Integrals, Chebyshev polynomials).. They are either evaluated using matrix-

• Several Pioneers of solving PDEs with finite-difference method (Lewis Fry Richardson, Richard Southwell, Richard Courant, Kurt Friedrichs, Hans Lewy, Peter Lax and John von

• As the space discetization is often imposed by considering the smallest seismic velocities in the medium and the highest frequencies, the CFL criterion determines the time

• By mixing finite-difference operators and pseudospectral operators in the different spatial directions, the method was used for interesting seismological problems (Furumura et

• Because of the grid densification at the boundaries of the Chebyshev collocation points very small time steps are required for stable simulations when n is large. This can be

In general, the numerical solution of boundary value problems is more difficult than that of initial value problems because the relatively simple approaches of propagating a solution

MIPS - Floating Point Instructions. Floating Point Operations are done

It should be stressed that the results are not restricted to lattice Boltzmann methods but can readily be applied to any other finite difference scheme (see [4] for various examples