13 citations · 27 across the 13 of their papers we have counts for
16 papers
Analysis of split exponential integrators for semilinear problems with noncommuting operators
Luca Battestini, Marco Caliari, Fabio Cassini
Splitting the exponential and exponential-like functions can significantly reduce the overall computational cost of exponential integrators, providing a strong motivation for their…
A tensor-based exponential integrator for diffusion--reaction equations in common curvilinear coordinates
Marco Caliari, Fabio Cassini
In this paper, we study a tensor-based method for the numerical solution of a class of diffusion--reaction equations defined on spatial domains that admit common curvilinear coordi…
Matrix- and tensor-oriented numerical schemes for the evolutionary space-fractional complex Ginzburg--Landau equation
Marco Caliari, Fabio Cassini
In this manuscript, we propose matrix- and tensor-oriented methods for the numerical solution of the multidimensional evolutionary space-fractional complex Ginzburg--Landau equatio…
On the convergence of split exponential integrators for semilinear parabolic problems
Marco Caliari, Fabio Cassini, Lukas Einkemmer +1
Splitting the exponential-like functions, which typically appear in exponential integrators, is attractive in many situations since it can dramatically reduce the computational…
The turnpike control in stochastic multi-agent dynamics: a discrete-time approach with exponential integrators
Fabio Cassini, Chiara Segala
In this manuscript, we study the turnpike property in stochastic discrete-time optimal control problems for interacting agents. Extending previous deterministic results, we show th…
Exponential quadrature rules for problems with time-dependent fractional source
Marco Caliari, Fabio Cassini
In this manuscript, we propose newly-derived exponential quadrature rules for stiff linear differential equations with time-dependent fractional sources in the form , with…
Efficient simulation of complex Ginzburg--Landau equations using high-order exponential-type methods
Marco Caliari, Fabio Cassini
In this paper, we consider the task of efficiently computing the numerical solution of evolutionary complex Ginzburg--Landau equations on Cartesian product domains with homogeneous…
Efficient third order tensor-oriented directional splitting for exponential integrators
Fabio Cassini
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with -dimension…
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…
Accelerating exponential integrators to efficiently solve semilinear advection-diffusion-reaction equations
Marco Caliari, Fabio Cassini, Lukas Einkemmer +1
In this paper we consider an approach to improve the performance of exponential Runge--Kutta integrators and Lawson schemes} in cases where the solution of a related, but usually m…
Exponential integrators for mean-field selective optimal control problems
Giacomo Albi, Marco Caliari, Elisa Calzola +1
In this paper we consider mean-field optimal control problems with selective action of the control, where the constraint is a continuity equation involving a non-local term and dif…
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…
Efficient 6D Vlasov simulation using the dynamical low-rank framework Ensign
Fabio Cassini, Lukas Einkemmer
Running kinetic simulations using grid-based methods is extremely expensive due to the up to six-dimensional phase space. Recently, it has been shown that dynamical low-rank algori…
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…