Related papers: Splitting methods for solution decomposition in no…
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…
Domain decomposition methods are essential in solving applied problems on parallel computer systems. For boundary value problems for evolutionary equations the implicit schemes are in common use to solve problems at a new time level…
The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the $H^{-1}$-gradient flow of the…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow can not be computed exactly. Instead, we use a numerical…
This paper proposes and analyzes a new operator splitting method for stochastic Maxwell equations driven by additive noise, which not only decomposes the original multi-dimensional system into some local one-dimensional subsystems, but also…
This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS…
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of a transport equation with additional growth and non-local…
We propose an abstract stochastic scheme for solving a broad range of monotone operator inclusion problems in Hilbert spaces. This framework allows for the introduction of stochasticity at several levels in monotone operator splitting…
In this paper we propose new averaged iterative algorithms designed for solving a split common fixed-point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used…
This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems…
We consider the Cauchy problem for a second-order evolution equation, in which the problem operator is the sum of two self-adjoint operators. The main feature of the problem is that one of the operators is represented in the form of 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…
We provide general product formulas for the solutions of non-autonomous abstract Cauchy problems. The main technical tool is the application of evolution semigroup methods, allowing the direct application of existing results on autonomous…
Splitting methods are widely used for solving initial value problems (IVPs) due to their ability to simplify complicated evolutions into more manageable subproblems which can be solved efficiently and accurately. Traditionally, these…
Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…
Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…
This work continues a line of works on developing partially explicit methods for multiscale problems. In our previous works, we have considered linear multiscale problems, where the spatial heterogeneities are at subgrid level and are not…
Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value…