18 citations · 80 across the 17 of their papers we have counts for
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Local Time-Stepping for the Shallow Water Equations using CFL Optimized Forward-Backward Runge-Kutta Schemes
Jeremy R. Lilly, Giacomo Capodaglio, Darren Engwirda +2
The Courant-Friedrichs-Lewy (CFL) condition is a well known, necessary condition for the stability of explicit time-stepping schemes that effectively places a limit on the size of…
CFL Optimized Forward-Backward Runge-Kutta Schemes for the Shallow Water Equations
Jeremy R. Lilly, Darren Engwirda, Giacomo Capodaglio +2
We present the formulation and optimization of a Runge-Kutta-type time-stepping scheme for solving the shallow water equations, aimed at substantially increasing the effective allo…
A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type
Manuel Klar, Giacomo Capodaglio, Marta D'Elia +3
Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the mai…
An asymptotically compatible coupling formulation for nonlocal interface problems with jumps
Christian Glusa, Marta D'Elia, Giacomo Capodaglio +2
We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak f…
Local time stepping for the shallow water equations in MPAS
Giacomo Capodaglio, Mark Petersen
We assess the performance of a set of local time-stepping (LTS) schemes for the shallow water equations implemented in the Model for Prediction Across Scales (MPAS). The goal of LT…
Efficient quadrature rules for finite element discretizations of nonlocal equations
Eugenio Aulisa, Giacomo Capodaglio, Andrea Chierici +1
In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main chal…
A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions
Giacomo Capodaglio, Marta D'Elia, Max Gunzburger +3
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a…
A computational study of preconditioning techniques for the stochastic diffusion equation with lognormal coefficient
Eugenio Aulisa, Giacomo Capodaglio, Guoyi Ke
We present a computational study of several preconditioning techniques for the GMRES algorithm applied to the stochastic diffusion equation with a lognormal coefficient discretized…
Piecewise polynomial approximation of probability density functions with application to uncertainty quantification for stochastic PDEs
Giacomo Capodaglio, Max Gunzburger
The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample s…
Approximation of probability density functions for PDEs with random parameters using truncated series expansions
Giacomo Capodaglio, Max Gunzburger, Henry P. Wynn
The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a tru…
Construction of h-refined continuous finite element spaces with arbitrary hanging node configurations and applications to multigrid algorithms
Eugenio Aulisa, Giacomo Capodaglio, Guoyi Ke
We present a novel approach for the construction of basis functions to be employed in selective or adaptive h-refined finite element applications with arbitrary-level hanging node…
Convergence estimates for multigrid algorithms with SSC smoothers and applications to overlapping domain decomposition
Eugenio Aulisa, Giorgio Bornia, Sara Calandrini +1
In this paper we study convergence estimates for a multigrid algorithm with smoothers of successive subspace correction (SSC) type, applied to symmetric elliptic PDEs. First, we re…