Computation of eigenvalues by numerical upscaling

Robust Numerical Upscaling at High Contrast

Robust Numerical Upscaling at High Contrast

On the Computation of Matrix Functions for Square Matrices Having Mixed Eigenvalues Using Numerical Hybrid Method

Abstract: In this paper, a hybrid numerical method for computing matrix functions of square matrices having mixed (distinct real and pure complex) eigenvalues is presented. The suggested technique is first stated and is then proved to be well defined through different stages. The theoretical analysis of the proposal method is then discussed. Some numerical examples are presented to validate the...

Continuous spectra and numerical eigenvalues

1. On numerical spectra for the linearized Burgers’ equation The stability of a traveling wave depends on the spectrum of a differential operator L obtained by linearization about the wave profile. As a simple example, consider Burgers’ equation ut = uxx − 1 2 (u)x, x ∈ R, t ≥ 0, with stationary solution U(x) = − tanh x 2 . Linearization about U(x) leads to the spectral problem Lu ≡ uxx − (Uu)x...

Parallel Computation of Eigenvalues of Real Matrices

Upscaling of Permeability Field of Fractured Rock System: Numerical Examples

When the permeability field of a given porous medium domain is heterogeneous by the existence of randomly distributed fractures such that numerical investigation becomes cumbersome, another level of upscaling may be required. That is such complex permeability field could be relaxed i.e., smoothed by constructing an effective permeability field. The effective permeability field is an approximati...