132 citations · 303 across the 16 of their papers we have counts for
12 papers · 1 filter
A second order directional split exponential integrator for systems of advection--diffusion--reaction equations
Marco Caliari, Fabio Cassini
We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection--diffusion--reaction equations in two and three space dimens…
Direction splitting of -functions in exponential integrators for -dimensional problems in Kronecker form
Marco Caliari, Fabio Cassini
In this manuscript, we propose an efficient, practical and easy-to-implement way to approximate actions of -functions for matrices with -dimensional Kronecker sum structure i…
A -mode approach for exponential integrators: actions of -functions of Kronecker sums
Marco Caliari, Fabio Cassini, Franco Zivcovich
We present a method for computing actions of the exponential-like -functions for a Kronecker sum of arbitrary matrices . It is based on the approximation of the int…
A -mode BLAS approach for multidimensional tensor-structured problems
Marco Caliari, Fabio Cassini, Franco Zivcovich
In this manuscript, we present a common tensor framework which can be used to generalize one-dimensional numerical tasks to arbitrary dimension by means of tensor product formu…
A -mode integrator for solving evolution equations in Kronecker form
Marco Caliari, Fabio Cassini, Lukas Einkemmer +2
In this paper, we propose a -mode integrator for computing the solution of stiff evolution equations. The integrator is based on a -dimensional splitting approach and uses ex…
An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs
Marco Caliari, Lukas Einkemmer, Alexander Moriggl +1
Rational exponential integrators (REXI) are a class of numerical methods that are well suited for the time integration of linear partial differential equations with imaginary eigen…
INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections
Marco Caliari, Simone Zuccher
Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a…
A splitting approach for the magnetic Schrödinger equation
Marco Caliari, Alexander Ostermann, Chiara Piazzola
The Schrödinger equation in the presence of an external electromagnetic field is an important problem in computational quantum mechanics. It also provides a nice example of a diffe…
Reliability of the time splitting Fourier method for singular solutions in quantum fluids
Marco Caliari, Simone Zuccher
We extensively study the numerical accuracy of the well-known time splitting Fourier spectral method for the approximation of singular solutions of the Gross-Pitaevskii equation. I…
The Leja method revisited: backward error analysis for the matrix exponential
Marco Caliari, Peter Kandolf, Alexander Ostermann +1
The Leja method is a polynomial interpolation procedure that can be used to compute matrix functions. In particular, computing the action of the matrix exponential on a given vecto…
Computing the first eigenpair for problems with variable exponents
Marcello Bellomi, Marco Caliari, Marco Squassina
We compute the first eigenpair for variable exponent eigenvalue problems. We compare the homogeneous definition of first eigenvalue with previous nonhomogeneous notions in the lite…
Numerical computation of soliton dynamics for NLS equations in a driving potential
Marco Caliari, Marco Squassina
We provide some numerical computations for the soliton dynamics of the nonlinear Schrödinger equation with an external potential. After computing the ground state solution of a…