Complex moments of the local power spectrum (CMP) are investigated in a multiscale context. The multiscale CMPs are shown to approximate well the 1D angular Fourier transform of the band in question. This observation is used to derive further properties of the power spectrum in terms of texture orientations or n-folded symmetry patterns. A method is presented to approximate the power spectrum u...

Abstract An efficient direct domain decomposition method is developed coupled with Poly-Sinc approximation over complex geometry. We solve 2D Poisson equations in L-Shaped geometry. The spatial domains of interest are decomposed into several non-overlapping rectangular subdomains. In each sub-domain, a Poly-Sinc collocation scheme is used to approximate the solution of the governing equation. S...

The development of numerical algorithms for modeling ow processes in large-scale highly heterogeneous formations is very challenging because the properties of natural geologic porous formations (e.g., permeability) display high variability levels and complex spatial correlation structures, which span a rich hierarchy of length scales. Thus, it is usually necessary to resolve a wide range of len...

In this note, we discuss iterative substructuring methods for a scalar elliptic model problem with a strongly varying diffusion coefficient that is typically discontinuous and exhibits large jumps. Opposed to earlier theory, we treat the case where the jumps happen on a small spatial scale and can in general not be resolved by a domain decomposition. We review the available theory of FETI metho...

We here propose a multiscale numerical method for the solution of stochastic partial differential equations with localized uncertainties. It is based on a multiscale domain decomposition method that exploits the localized side of uncertainties and incidentally improves the conditioning of the problem by operating a separation of scales. An efficient iterative algorithm is proposed that requires...

High performance computing has undergone a radical transformation during the past decade. Though monolithic supercomputers continue to be built with significantly increased computing power, geographically distributed computing resources are now routinely linked using high-speed networks to address a broad range of computationally complex problems. These confederated resources are referred to co...

In this paper, we study multiscale finite element methods (MsFEMs) using basis functions that provide an optimal convergence in domain decomposition methods. We consider second order elliptic equations with highly variable coefficients. Both multiscale finite element and domain decomposition methods (considered here) use coarse spaces to achieve efficiency and robustness. In MsFEMs, the spatial...

A convergence theory is presented for a substructuring preconditioner based on constrained energy minimization concepts. The preconditioner is formulated as an Additive Schwarz method and analyzed by building on existing results for Balancing Domain Decomposition. The main result is a bound on the condition number based on inequalities involving the matrices of the preconditioner. Estimates of ...

This paper proposes a voice decomposition method based on voice model. Using correlation distance as a criterion frequency domain decomposition is formulated. For a pair of correlation coe cient vectors minimizing powers of spectra is characterized using quadratic programming problem with constraint, where values of powers are non-negative. The solution of the problem without constraint is calc...