We introduce an ultraweak space-time variational formulation for the wave equation, prove
its well-posedness (even in the case of minimal regularity) and optimal inf-sup stability …

The $ p $-step backwards difference formula (BDF) for solving the system of ODEs can result
in a kind of all-at-once linear systems, which are solved via the parallel-in-time …

Various iterative eigenvalue solvers have been developed to compute parts of the spectrum
for a large sparse matrix, including the power method, Krylov subspace methods, contour …

In this paper, we study a direct parallel-in-time (PinT) algorithm for first-and second-order
time-dependent differential equations. We use a second-order boundary value method as …

This work is concerned with the numerical solution of large-scale symmetric positive definite
matrix equations of the form $ A_1XB_1^\top+ A_2XB_2^\top+\dots+ A_\ell X B_\ell^\top= F …

This work is concerned with linear matrix equations that arise from the space-time
discretization of time-dependent linear partial differential equations (PDEs). Such matrix …

Time-parallel time integration has received a lot of attention in the high performance
computing community over the past two decades. Indeed, it has been shown that parallel-in …

Thanks to its great potential in reducing both computational cost and memory requirements,
combining sketching and Krylov subspace techniques has attracted a lot of attention in the …

Thanks to its great potential in reducing both computational cost and memory requirements,
combining sketching and Krylov subspace techniques has attracted a lot of attention in the …

For the spatial discretization of elliptic and parabolic partial differential equations (PDEs), we
provide a Matrix-Oriented formulation of the classical Finite Element Method, called MO …