719 citations · 972 across the 29 of their papers we have counts for
31 papers
Robust domain decomposition methods for high-contrast multiscale problems on irregular domains with virtual element discretizations
Juan G. Calvo, Juan Galvis
Our research focuses on the development of domain decomposition preconditioners tailored for second-order elliptic partial differential equations. Our approach addresses two major…
Higher order derivatives of the adjugate matrix and the Jordan form
Jorge I. Rubiano-Murcia, Juan Galvis
In this short note, we show that the higher-order derivatives of the adjugate matrix $\mbox{Adj}(z-A)$, are related to the nilpotent matrices and projections in the Jordan decompos…
Mathematical modelling of proton migration in Earth mantle
Vadim Bobrovskiy, Juan Galvis, Alexey Kaplin +3
In the study, we address the mathematical problem of proton migration in the Earth's mantle and suggest a prototype for exploring the Earth's interior to map the effects of superio…
Finite difference and finite element methods for partial differential equations on fractals
Fernando Contreras, Juan Galvis
In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. In particular, we consider the strong form of the equation…
A note on averaging prediction accuracy, Green's functions and other kernels
J. Galvis, Freddy Hernández-Romero, Francisco Gómez
We present the mathematical context of the predictive accuracy index and then introduce the definition of integral average transform. We establish the relation of our definition wi…
Natural Factor Based Solvers
O. Andrés Cuervo, Juan Galvis, Marcus Sarkis
We consider parametric families of partial differential equations--PDEs where the parameter modifies only the (1,1) block of a saddle point matrix product of a discretization b…
Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems
Miguel Zambrano, Sintya Serrano, Boyan S. Lazarov +1
The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization pro…
On the conservation properties in multiple scale coupling and simulation for Darcy flow with hyperbolic-transport in complex flows
Juan Galvis, Eduardo Abreu, Ciro Diaz +1
We present and discuss a novel approach to deal with conservation properties for the simulation of nonlinear complex porous media flows in the presence of: 1) multiscale heterogene…
On condition numbers of symmetric and nonsymmetric domain decomposition methods
Juan Galvis
Using oblique projections and angles between subspaces we write condition number estimates for abstract nonsymmetric domain decomposition methods. In particular, we consider a rest…
Numerical upscaling of the free boundary dam problem in multiscale high-contrast media
Juan Galvis, Carlos Vásquez, Luis F. Contreras
In this paper, we address the numerical homogenization approximation of a free-boundary dam problem posed in a heterogeneous media. More precisely, we propose a generalized multisc…
A convergence analysis of Generalized Multiscale Finite Element Methods
Eduardo Abreu, Ciro Diaz, Juan Galvis
In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We ob…
On overlapping domain decomposition methods for high-contrast multiscale problems
Juan Galvis, Eric Chung, Yalchin Efendiev +1
We review some important ideas in the design and analysis of robust overlapping domain decomposition algorithms for high-contrast multiscale problems and propose a domain decomposi…
A Monte Carlo approach to computing stiffness matrices arising in polynomial chaos approximations
Juan Galvis, O. Andres Cuervo
We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required e…
On high-order conservative finite element methods
Eduardo Abreu, Ciro Diaz, Juan Galvis +1
A new high-order conservative finite element method for Darcy flow is presented. The key ingredient in the formulation is a volumetric, residual-based, based on Lagrange multiplier…
A mass conservative generalized multiscale finite element method applied to two-phase flow in heterogeneous porous media
Michael Presho, Juan Galvis
In this paper, we propose a method for the construction of locally conservative flux fields through a variation of the Generalized Multiscale Finite Element Method (GMsFEM). The fl…
Delta shock wave for a hyperbolic system of conservation laws
Richard De la cruz, Juan C. Juajibioy, Juan Galvis +1
We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. This systems it is a simplification of a recently propose system of…
Asymptotic Expansions for High-Contrast Linear Elasticity
Leonardo A. Poveda, Sebastian Huepo, Victor M. Calo +1
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous ela…
Localized Harmonic Characteristic Basis Functions for Multiscale Finite Element Methods
Leonardo A. Poveda, Sebastian Huepo, Victor M. Calo +1
We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a…
Randomized Oversampling for Generalized Multiscale Finite Element Methods
Victor M. Calo, Y. Efendiev, Juan Galvis +1
In this paper, we study the development of efficient multiscale methods for flows in heterogeneous media. Our approach uses the Generalized Multiscale Finite Element (GMsFEM) frame…
Global-Local Nonlinear Model Reduction for Flows in Heterogeneous Porous Media
Manal Alotaibi, Victor M. Calo, Yalchin Efendiev +2
In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite El…
Multiscale Empirical Interpolation for Solving Nonlinear PDEs using Generalized Multiscale Finite Element Methods
Victor Calo, Yalchin Efendiev, Juan Galvis +1
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interp…
A Generalized Multiscale Finite Element Method for the Brinkman Equation
Guanglian Li, Juan Galvis, Ke Shi
In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Gener…
The analysis of FETI-DP preconditioner for full DG discretization of elliptic problems
Maksymilian Dryja, Juan Galvis, Marcus Sarkis
In this paper a discretization based on discontinuous Galerkin (DG) method for an elliptic two-dimensional problem with discontinuous coefficients is considered. The problem is pos…
On the Riemann problem for the simplified Bouchut-Boyaval system
Richard A. De la cruz Guerrero, Juan Galvis, Juan Carlos Juajibioy +1
In this paper we study the one-dimensional Riemann problem for a new hyperbolic system of three conservation laws of Temple class. This systems it is a simplification of a recently…