Related papers: Improving the stability and efficiency of high-ord…
We are concerned with the numerical solution obtained by splitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real coefficients necessarily involve negative coefficients. It…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
Integral deferred correction (IDC) methods have been shown to be an efficient way to achieve arbitrary high order accuracy and possess good stability properties. In this paper, we construct high order operator splitting schemes using the…
We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…
This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We first employ classical Taylor expansion which, after some…
Prior to the recent development of symplectic integrators, the time-stepping operator $\e^{h(A+B)}$ was routinely decomposed into a sum of products of $\e^{h A}$ and $\e^{hB}$ in the study of hyperbolic partial differential equations. In…
In this article we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an…
The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…
In this paper, we develop a class of samplers for the diffusion model using the operator-splitting technique. The linear drift term and the nonlinear score-driven drift of the probability flow ordinary differential equation are split and…
For systems of the form $\dot q = M^{-1} p$, $\dot p = -Aq+f(q)$, common in many applications, we analyze splitting integrators based on the (linear/nonlinear) split systems $\dot q = M^{-1} p$, $\dot p = -Aq$ and $\dot q = 0$, $\dot p =…
Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly…
The port-Hamiltonian approach presents an energy-based modeling of dynamical systems with energy-conservative and energy-dissipative parts as well as an interconnection over the so-called ports. In this paper, we apply an operator splitting…
In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of…
In contrast with the diffusion equation which smoothens the initial data to $C^\infty$ for $t>0$ (away from the corners/edges of the domain), the subdiffusion equation only exhibits limited spatial regularity. As a result, one generally…
Accurately simulating long-time dynamics of many-body systems is a challenge in both classical and quantum computing due to the accumulation of Trotter errors. While low-order Trotter-Suzuki decompositions are straightforward to implement,…
In the simulation of differential-algebraic equations (DAEs), it is essential to employ numerical schemes that take into account the inherent structure and maintain explicit or hidden algebraic constraints without altering them. This paper…
We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several…
We consider quadrature formulas of high order in time based on Radau-type, L-stable implicit Runge-Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs…