Related papers: Operator splitting for semi-explicit differential-…
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…
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…
Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…
Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such…
A dynamic iteration scheme for linear differential-algebraic port-Hamil\-tonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no…
In this paper, we develop high-order splitting methods for linear port-Hamiltonian systems, focusing on preserving their intrinsic structure, particularly the dissipation inequality. Port-Hamiltonian systems are characterized by their…
In this work we study operator splitting methods for a certain class of coupled abstract Cauchy problems, where the coupling is such that one of the problems prescribes a "boundary type" extra condition for the other one. The theory of…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular…
Infinite-dimensional differential algebraic equations (short DAEs) with input and output are studied. The concepts of operator nodes and system nodes are extended to systems which additionally may include algebraic constraints.…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE…
Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
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…
Different representations of dissipative Hamiltonian and port-Hamiltonian differential-algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between the different…
Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…
Operator-splitting methods are widely used to solve differential equations, especially those that arise from multi-scale or multi-physics models, because a monolithic (single-method) approach may be inefficient or even infeasible. The most…
On the basis of additive schemes (splitting schemes) we construct efficient numerical algorithms to solve approximately the initial-boundary value problems for systems of time-dependent partial differential equations (PDEs). In many applied…