Abstract The full Maxwell equations in the unbounded three-dimensional space coupled to Landau–Lifshitz–Gilbert equation serve as a well-tested model for ferromagnetic materials. We propose weak formulation of system based on boundary integral exterior equations. show existence and partial uniqueness solution new numerical algorithm finite elements spatial discretization with backward Euler con...

In this article, we derive a new, fast, and robust preconditioned iterative solution strategy for the all-at-once of optimal control problems with time-dependent PDEs as constraints, including heat equation non-steady convection–diffusion equation. After applying an optimize-then-discretize approach, one is faced continuous first-order optimality conditions consisting coupled system PDEs. As op...

When differential-algebraic equations of index 3 or higher are solved with backward differentiation formulas, the solution can have gross errors in the first few steps, even if the initial values are equal to the exact solution and even if the stepsize is kept constant. This raises the question of what are consistent initial values for the difference equations. Here we study how to change the e...

We propose a multi-step Richardson-Romberg extrapolation method for the computation of expectations Ef(X T ) of a diffusion (Xt)t∈[0,T ] when the weak time discretization error induced by the Euler scheme admits an expansion at an order R ≥ 2. The complexity of the estimator grows as R (instead of 2) and its variance is asymptotically controlled by considering some consistent Brownian increment...

A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with a Balancing Domain Decomposition by Constraints (BDDC) preconditioner and inexact local solvers to provide an efficient solution technique for large-scale, convection-dominated problems. The algorithm is applied to the linear system arising from the discretization of the two-dimensional advection-diffusion ...

We show that the m-dimensional Euler–Manakov top on so∗(m) can be represented as a Poisson reduction of an integrable Hamiltonian system on a symplectic extended Stiefel variety V̄(k,m), and present its Lax representation with a rational parameter. We also describe an integrable two-valued symplectic map B on the 4dimensional variety V(2, 3). The map admits two different reductions, namely, to t...

We show that the m-dimensional Euler–Manakov top on so∗(m) can be represented as a Poisson reduction of an integrable Hamiltonian system on a symplectic extended Stiefel variety V̄(k,m), and present its Lax representation with a rational parameter. We also describe an integrable two-valued symplectic map B on the 4dimensional variety V(2, 3). The map admits two different reductions, namely, to t...

We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the f...

We show that the discretized configuration space of k points in the n-simplex is homotopy equivalent to a wedge of spheres of dimension n− k+1. This space is homeomorphic to the order complex of the poset of ordered partial partitions of {1, . . . , n+1} with exactly k parts. We also compute the Euler characteristic in two different ways, thereby obtaining a topological proof of a combinatorial...