86 citations · 150 across the 14 of their papers we have counts for
16 papers · 1 filter
Fast solution of a phase-field model of pitting corrosion
Gianluca Frasca-Caccia, Dajana Conte, Beatrice Paternoster
Excessive computational times represent a major challenge in the solution of corrosion models, limiting their practical applicability, e.g., as a support to predictive maintenance.…
Arbitrarily high-order energy-conserving methods for Hamiltonian problems with quadratic holonomic constraints
P. Amodio, L. Brugnano, G. Frasca-Caccia +1
In this paper, we define arbitrarily high-order energy-conserving methods for Hamiltonian systems with quadratic holonomic constraints. The derivation of the methods is made within…
Numerical conservation laws of time fractional diffusion PDEs
Angelamaria Cardone, Gianluca Frasca-Caccia
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that sa…
Exponentially fitted methods with a local energy conservation law
Dajana Conte, Gianluca Frasca-Caccia
A new exponentially fitted version of the Discrete Variational Derivative method for the efficient solution of oscillatory complex Hamiltonian Partial Differential Equations is pro…
Exponentially fitted methods that preserve conservation laws
Dajana Conte, Gianluca Frasca-Caccia
The exponential fitting technique uses information on the expected behaviour of the solution of a differential problem to define accurate and efficient numerical methods. In partic…
Optimal parameters for numerical solvers of PDEs
Gianluca Frasca-Caccia, Pranav Singh
In this paper we introduce a procedure for identifying optimal methods in parametric families of numerical schemes for initial value problems in partial differential equations. The…
A new framework for polynomial approximation to differential equations
Luigi Brugnano, Gianluca Frasca-Caccia, Felice Iavernaro +1
In this paper we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework, initially devised for the…
A new technique for preserving conservation laws
G. Frasca-Caccia, P. E. Hydon
This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We prove that for one spatial d…
Line Integral solution of Hamiltonian PDEs
Luigi Brugnano, Gianluca Frasca-Caccia, Felice Iavernaro
In this paper, we report about recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs), by using energy-conserving line integral methods in t…
Numerical preservation of multiple local conservation laws
Gianluca Frasca-Caccia, Peter E. Hydon
There are several well-established approaches to constructing finite difference schemes that preserve global invariants of a given partial differential equation. However, few of th…
Locally conservative finite difference schemes for the modified KdV equation
Gianluca Frasca-Caccia, Peter E. Hydon
Finite difference schemes that preserve two conservation laws of a given partial differential equation can be found directly by a recently-developed symbolic approach. Until now, t…
Bespoke finite difference methods that preserve two local conservation laws of the modified KdV equation
Gianluca Frasca-Caccia
By exploiting the fact that conservation laws form the kernel of a discrete Euler operator, we use a recently introduced symbolic-numeric approach to construct a new class of finit…
Simple bespoke preservation of two conservation laws
Gianluca Frasca-Caccia, Peter E. Hydon
Conservation laws are among the most fundamental geometric properties of a partial differential equation (PDE), but few known finite difference methods preserve more than one conse…
Energy conserving methods for Hamiltonian PDEs based on spectral space decomposition
Luigi Brugnano, Gianluca Frasca Caccia, Felice Iavernaro
In this paper we discuss energy conservation issues related to the numerical solution of the nonlinear wave equation, when a Fourier expansion is considered for the space discretiz…
Energy conservation issues in the numerical solution of the semilinear wave equation
Luigi Brugnano, Gianluca Frasca Caccia, Felice Iavernaro
In this paper we discuss energy conservation issues related to the numerical solution of the nonlinear wave equation. As is well known, this problem can be cast as a Hamiltonian sy…
Efficient implementation of geometric integrators for separable Hamiltonian problems
Luigi Brugnano, Gianluca Frasca Caccia, Felice Iavernaro
We here investigate the efficient implementation of the energy-conserving methods named Hamiltonian Boundary Value Methods (HBVMs) recently introduced for the numerical solution of…