Related papers: The Parallel Subdomain-Levelset Deflation Method i…
We examine the use of a two-level deflation preconditioner combined with GMRES to locally solve the subdomain systems arising from applying domain decomposition methods to Helmholtz problems. Our results show that the direct solution method…
In \emph{Wang et al., A Shifted Laplace Rational Filter for Large-Scale Eigenvalue Problems}, the SLRF method was proposed to compute all eigenvalues of a symmetric definite generalized eigenvalue problem lying in an interval on the real…
Accurate and efficient numerical simulation of unconventional reservoirs is challenging. Long periods of transient flow and steep potential gradients occur due to the extreme conductivity contrast between matrix and fracture. Detailed…
Fluid injection and production cause changes in reservoir pressure, which result in deformations in the subsurface. This phenomenon is particularly important in reservoirs with abundant fractures and faults because the induced slip and…
The computation time for reservoir simulation is dominated by the linear solver. The sets of linear equations which arise in reservoir simulation have two distinctive features: the problems are usually highly anisotropic, with a dominant…
We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time-lapse observed seismic data by coupling full-waveform inversion, subsurface flow processes, and rock physics models. For…
Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor…
Shear dilation based hydraulic stimulations enable exploitation of geothermal energy from reservoirs with inadequate initial permeability. While contributing to enhancing the reservoir's permeability, hydraulic stimulation processes may…
The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…
This paper presents our work on developing parallel computational methods for two-phase flow on modern parallel computers, where techniques for linear solvers and nonlinear methods are studied and the standard and inexact Newton methods are…
In this paper we give a profound insight into the computation capability of delay-based reservoir computing via an eigenvalue analysis. We concentrate on the task-independent memory capacity to quantify the reservoir performance and compare…
For a quadratic matrix polynomial associated with a damped mass-spring system there are three types of critical eigenvalues, the eigenvalues $\infty$ and $0$ and the eigenvalues on the imaginary axis. All these are on the boundary of the…
Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to the flattest local minimizer can be found due to the implicit regularization of stochastic gradient descent. This…
There are two usual computational methods for linear (waves and instabilities) problem: eigenvalue (dispersion relation) solver and initial value solver. In fact, we can introduce an idea of the combination of them, i.e., we keep time…
This paper proposes a rational filtering domain decomposition technique for the solution of large and sparse symmetric generalized eigenvalue problems. The proposed technique is purely algebraic and decomposes the eigenvalue problem…
This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR)…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
Hydraulic stimulation of geothermal reservoirs in low-permeability basement and crystalline igneous rock can enhance permeability by reactivation and shear dilation of existing fractures. The process is characterized by interaction between…
Modeling groundwater flow in three-dimensional fractured crystalline media requires accounting for strong spatial heterogeneity induced by fractures. Fine-scale discrete fracture-matrix (DFM) simulations can capture this complexity but are…
The topology of a network associated with a reservoir computer is often taken so that the connectivity and the weights are chosen randomly. Optimization is hardly considered as the parameter space is typically too large. Here we investigate…