128 citations · 223 across the 15 of their papers we have counts for
20 papers
Semi-Algebraic Mode Analysis For Finite Element Discretisations Of The Heat Equation
A. Mesforush, N. Habibi, F. Gasper +1
In this work, a semialgebraic mode analysis (SAMA) is proposed for investigating the convergence of a multigrid waveform relaxation method applied to the Finite Element (FE) discre…
Multigrid solvers for multipoint flux approximations of the Darcy problem on rough quadrilateral grids
Andrés Arrarás, Francisco J. Gaspar, Laura Portero +1
In this work, an efficient blackbox-type multigrid method is proposed for solving multipoint flux approximations of the Darcy problem on logically rectangular grids. The approach i…
A Local Fourier Analysis for Additive Schwarz Smoothers
Álvaro Pé de la Riva, Carmen Rodrigo, Francisco J. Gaspar +3
In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general frame…
A two level method for isogeometric discretizations
Álvaro Pé de la Riva, Carmen Rodrigo, Francisco J. Gaspar
Isogeometric Analysis (IGA) is a computational technique for the numerical approximation of partial differential equations (PDEs). This technique is based on the use of spline-type…
Robust preconditioners for a new stabilized discretization of the poroelastic equations
James H. Adler, Francisco J. Gaspar, Xiaozhe Hu +3
In this paper, we present block preconditioners for a stabilized discretization of the poroelastic equations developed in [45]. The discretization is proved to be well-posed with r…
A parametric acceleration of multilevel Monte Carlo convergence for nonlinear variably saturated flow
Prashant Kumar, Carmen Rodrigo, Francisco J. Gaspar +1
We present a multilevel Monte Carlo (MLMC) method for the uncertainty quantification of variably saturated porous media flow that are modeled using the Richards' equation. We propo…
Geometric multigrid methods for Darcy-Forchheimer flow in fractured porous media
Andrés Arrarás, Francisco J. Gaspar, Laura Portero +1
In this paper, we present a monolithic multigrid method for the efficient solution of flow problems in fractured porous media. Specifically, we consider a mixed-dimensional model w…
Monolithic mixed-dimensional multigrid methods for single-phase flow in fractured porous media
Andrés Arrarás, Francisco J. Gaspar, Laura Portero +1
This paper deals with the efficient numerical solution of single-phase flow problems in fractured porous media. A monolithic multigrid method is proposed for solving two-dimensiona…
An efficient multigrid solver for isogeometric analysis
Álvaro Pé de la Riva, Carmen Rodrigo, Francisco J. Gaspar
The design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to…
On local Fourier analysis of multigrid methods for PDEs with jumping and random coefficients
Prashant Kumar, Carmen Rodrigo, Francisco J. Gaspar +1
In this paper, we propose a novel non-standard Local Fourier Analysis (LFA) variant for accurately predicting the multigrid convergence of problems with random and jumping coeffici…
On the validity of the local Fourier analysis
Carmen Rodrigo, Francisco J. Gaspar, Ludmil T. Zikatanov
Local Fourier analysis (LFA) is a useful tool in predicting the convergence factors of geometric multigrid methods (GMG). As is well known, on rectangular domains with periodic bou…
New stabilized discretizations for poroelasticity and the Stokes' equations
Carmen Rodrigo, Xiaozhe Hu, Peter Ohm +3
In this work, we consider the popular P1-RT0-P0 discretization of the three-field formulation of Biot's consolidation problem. Since this finite-element formulation does not satisf…
Using hierarchical matrices in the solution of the time-fractional heat equation by multigrid waveform relaxation
Xiaozhe Hu, Carmen Rodrigo, Francisco J. Gaspar
This work deals with the efficient numerical solution of the time-fractional heat equation discretized on non-uniform temporal meshes. Non-uniform grids are essential to capture th…
Robust Block Preconditioners for Biot's Model
James H. Adler, Francisco J. Gaspar, Xiaozhe Hu +2
In this paper, we design robust and efficient block preconditioners for the two-field formulation of Biot's consolidation model, where stabilized finite-element discretizations are…
Multigrid waveform relaxation for the time-fractional heat equation
Francisco J. Gaspar, Carmen Rodrigo
In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators,…
A Nonconforming Finite Element Method for the Biot's Consolidation Model in Poroelasticity
Xiaozhe Hu, Carmen Rodrigo, Francisco J. Gaspar +1
A stable finite element scheme that avoids pressure oscillations for a three-field Biot's model in poroelasticity is considered. The involved variables are the displacements, fluid…
On a local Fourier analysis for overlapping block smoothers on triangular grids
Carmen Rodrigo, Francisco J. Gaspar, Francisco J. Lisbona
A general local Fourier analysis for overlapping block smoothers on triangular grids is presented. This analysis is explained in a general form for its application to problems with…
Stability and Monotonicity for Some Discretizations of the Biot's Model
Carmen Rodrigo, Francisco Gaspar, Xiaozhe Hu +1
We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully disc…
A Finite Element Framework for Some Mimetic Finite Difference Discretizations
Carmen Rodrigo, Francisco Gaspar, Xiaozhe Hu +1
In this work we derive equivalence relations between mimetic finite difference schemes on simplicial grids and modified Nédélec-Raviart-Thomas finite element methods for model prob…
Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive coarsening
James Brannick, Xiaozhe Hu, Carmen Rodrigo +1
We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element dis…