9 papers
Condition numbers of block Toeplitz matrices and stability of space-time IgA approximations for the wave and Schrödinger equations
Manuel Bogoya, Albrecht Böttcher, Matteo Ferrari +2
In previous work by several authors, the behavior of the condition numbers of banded Toeplitz matrices was studied as the matrix size tends to infinity. In the present contribution…
A space-time sparse-grid method for the wave equation
Matteo Ferrari, Andrea Moiola, Chiara Perinati +1
We develop a fast space-time numerical scheme for approximating solutions to the linear wave equation. The approach is based on the sparse-grid combination technique applied to a c…
Stability, convergence, and geometric properties of second-order-in-time space-time discretizations for linear and semilinear wave equations
Matteo Ferrari, Ilaria Perugia, Enrico Zampa
We revisit second-order-in-time space-time discretizations of the linear and semilinear wave equations by establishing precise equivalences with first-order-in-time formulations. F…
Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation
Matteo Ferrari, Ilaria Perugia, Enrico Zampa
In this paper, we present a conforming space-time discretization of the wave equation based on a first-order-in-time variational formulation with exponential weights in time. We an…
A matrix-based approach to the stability of a space-time isogeometric method for the linear Schrödinger equation
Matteo Ferrari, Sergio Gómez
We propose a space-time isogeometric finite element method for the linear Schrödinger equation, and establish its unconditional stability through a matrix-based analysis. Although…
Intrinsic unconditional stability in space-time isogeometric approximation of the acoustic wave equation in second-order formulation
Matteo Ferrari, Ilaria Perugia
We present a novel space-time isogeometric discretization of the acoustic wave equation in second-order formulation that is intrinsically unconditionally stable. The method relies…
Unconditionally stable space-time isogeometric discretization for the wave equation in Hamiltonian formulation
Matteo Ferrari, Sara Fraschini, Gabriele Loli +1
We consider a family of conforming space-time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines. In contrast wit…
Some properties of a modified Hilbert transform
Matteo Ferrari
Recently, Steinbach et al. introduced a novel operator , known as the modified Hilbert transform. This operator has shown its significance in…
Stability of conforming space-time isogeometric methods for the wave equation
Matteo Ferrari, Sara Fraschini
We consider a family of conforming space-time finite element discretizations for the wave equation based on splines of maximal regularity in time. Traditional techniques may requir…