Related papers: An implicit split-operator algorithm for the nonli…
Supported by the recent contributions in multiple branches, the first-order splitting algorithms became central for structured nonsmooth optimization. In the large-scale or noisy contexts, when only stochastic information on the smooth part…
In this paper, we introduce a system of split variational inequality problems in real Hilbert spaces. Using projection method, we propose an iterative algorithm for the system of split variational inequality problems. Further, we prove that…
In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level…
This paper deals with the application of probabilistic time integration methods to semi-explicit partial differential-algebraic equations of parabolic type and its semi-discrete counterparts, namely semi-explicit differential-algebraic…
We elaborate further on the metric representation that is obtained by transferring the time-dependence from a Hermitian Hamiltonian to the metric operator in a related non-Hermitian system. We provide further insight into the procedure on…
Symplectic integration algorithms have become popular in recent years in long-term orbital integrations because these algorithms enforce certain conservation laws that are intrinsic to Hamiltonian systems. For problems with large variations…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
We analyse the scattering operator associated with the defocusing nonlinear Schr{\"o}dinger equation which captures the evolution of solutions over an infinite time-interval under the nonlinear flow of this equation. The asymptotic nature…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
The filtered Lie splitting scheme is an established method for the numerical integration of the periodic nonlinear Schr\"{o}dinger equation at low regularity. Its temporal convergence was recently analyzed in a framework of discrete…
In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and Lipschitz continuous operator and a cocoercive operator. Each…
We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…
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…
Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…
We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation.…
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…
A single-step high-order implicit time integration scheme for the solution of transient and wave propagation problems is presented. It is constructed from the Pad\'e expansions of the matrix exponential solution of a system of first-order…
The numerical solution of a linear Schr\"odinger equation in the semiclassical regime is very well understood in a torus $\mathbb{T}^d$. A raft of modern computational methods are precise and affordable, while conserving energy and…
In this paper, we develop a novel class of linear energy-preserving integrating factor methods for the 2D nonlinear Schr\"odinger equation with wave operator (NLSW), combining the scalar auxiliary variable approach and the integrating…