Related papers: Schur Decomposition for Stiff Differential Equatio…
A distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the efficient and accurate solution…
We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of…
We introduce a discrete delayed exponential depending on sequence of matrices. This discrete matrix gives a representation of a solution to the Cauchy problem for a discrete linear system with pure delay with sequence of matrices. We…
Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
Many interesting physical problems described by systems of hyperbolic conservation laws are stiff, and thus impose a very small time-step because of the restrictive CFL stability condition. In this case, one can exploit the superior…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
A parareal algorithm based on an exponential $\theta$-scheme is proposed for the stochastic Schr\"odinger equation with weak damping and additive noise. It proceeds as a two-level temporal parallelizable integrator with the exponential…
Stiff and chaotic differential equations are challenging for time-stepping numerical methods. For explicit methods, the required time step resolution significantly exceeds the resolution associated with the smoothness of the exact solution…
Schur Polynomials are families of symmetric polynomials that have been classically studied in Combinatorics and Algebra alike. They play a central role in the study of Symmetric functions, in Representation theory [Sta99], in Schubert…
Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
We present an algorithm of the reduction of the differential equations for master integrals the Fuchsian form with the right-hand side matrix linearly depending on dimensional regularization parameter $\epsilon$. We consider linear…
We note a fact that stiff systems or differential equations that have highly oscillatory solutions cannot be solved efficiently using conventional methods. In this paper, we study two new classes of exponential Runge-Kutta (ERK) integrators…
The solution of many physical evolution equations can be expressed as an exponential of two or more operators acting on initial data. Accurate solutions can be systematically derived by decomposing the exponential in a product form. For…
In this paper a technique is suggested to integrate linear initial boundary value problems with exponential quadrature rules in such a way that the order in time is as high as possible. A thorough error analysis is given for both the…
Physics-based animation of soft or rigid bodies for real-time applications often suffers from numerical instabilities. We analyse one of the most common sources of unwanted behaviour: the numerical integration strategy. To assess the impact…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…