21 papers · ranked by Valyu relevance
Petra Csomós, Matthias Ehrhardt, Bálint Farkas
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 sub-problems prescribes a "boundary type" extra condition for the other one. The theory of one-sided coupled operator matrices provides an excellent framework to study the…
Xianglong Duan, Chaoyu Quan, Jiang Yang, Zijing Zhu
The operator splitting method has been widely used to solve differential equations by splitting the equation into more manageable parts. In this work, we resolves a long-standing problem—how to establish the stability of multi-product expansion (MPE) splitting methods with negative weights. The difficulty occurs…
Jürgen Geiser
In this paper, we contribute operator-splitting methods improved by the Zassenhaus product for the numerical solution of linear partial differential equations. We address iterative splitting methods, that can be improved by means of the Zassenhaus product formula, which is a sequnential splitting scheme. The coupling…
Andreas Frommer, Michael Günther, Björn Liljegren-Sailer, Nicole Marheineke
'Nicole Marheineke'] Abstract 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 that treats the energy-conservative and…
Jaemin Shin, Hyun Geun Lee, June‐Yub Lee
The Allen–Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of the original equation using the solutions of the subproblems. Unlike the first and…
András Bátkai, Petra Csomós, Bálint Farkas
The present paper investigates a special operator splitting for a class of nonautonomous delay differential equations. This method, which can be applied to equations with distributed delays very effectively, was first investigated in Csom´os and Nickel [5] and in B´atkai, Csom´os and Nickel [2] in the autonomous case.…
Winfried Auzinger, Harald Hofstätter, David Ketcheson, Othmar Koch
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent…
Iain Hepburn, Weiliang Chen, Erik De Schutter
Parallelization is vital in the future of spatial stochastic simulation and an important component of the Human Brain Project [1]. There are some unique challenges to be faced for simulators based on unstructured meshes such as STEPS [2] and finding the most accurate yet scalable solution for different biological…
Eskil Hansen, Erik Henningsson
We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our analysis is conducted by first casting the domain decomposition procedure into a…
Keneth Adrian P. Dagal
This paper introduces a new equation for rewriting two unit fractions to another two unit fractions. This equation is useful for optimizing the elements of an Egyptian Fraction. Parity of the elements of the Egyptian Fractions are also considered. And lastly, the statement that all rational numbers can be represented…
Andrew Simmonett, Bernard Brooks, Thomas Darden
Evaluation of noncovalent electrostatic interactions is the dominant bottleneck in classical molecular dynamics simulations, and evaluation of Coulombic matrix elements similarly limits quantum mechanical self consistent field calculations. These difficulties are a result of the Coulomb operator’s slow decay, which…
Authors not listed
Classical molecular dynamics (MD) simulation is the most computationally efficient way to model large molecular systems atomistically for extended periods; however, due to fixed forcefield parameters, incorporating on-the-fly quantum reactions is not straightforward. Reactive Step-Based Molecular Dynamics (RSMD) is a…
Francisco J. Aragón-Artacho, Radu I. Boţ, David Torregrosa-Belén
In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators. Our main contribution is establishing the first primal-dual splitting algorithm…
Rajorshi Paul, Kevin S. Zhang, Myra Kurosu Jalil, Nicolas Castaño + 2 more
Stentor coeruleus, a single-cell ciliated protozoan, is a model organism for wound healing and regeneration studies. Despite Stentor’s large size (up to 2 mm in extended state), microdissection of Stentor remains challenging. In this work, we describe a hydrodynamic cell splitter, consisting of a cross junction…
Fahad Ahmed, Hattan Abutarboush, Naveed Ashraf, Tayeb A. Denidni + 1 more
'Farooq A. Tahir'] A multifunctional beam splitting frequency selective surface (FSS) is modeled, analyzed, and tested in transmission and reflection modes. The proposed FSS comprises a C-shaped split-ring resonator designed and fabricated on an ultrathin, flexible polyimide material. When a linearly polarized incident…
Gang Xu, Tianai Zhou, Xiu-Bo Chen, Xiaojun Wang + 1 more
Quantum information splitting (QIS) provides an idea for transmitting the quantum state through a classical channel and a preshared quantum entanglement resource. This paper presents a new scheme for QIS based on a five-qubit cluster state and a Bell state. In this scheme, the sender transmits the unknown three-qubit…
Manik Rajora, Pan Zou, Yao Guang Yang, Zhi Wen Fan + 4 more
'Wen Chieh Wu' 'Beizhi Li' 'Steven Y. Liang'] It can be observed from the experimental data of different processes that different process parameter combinations can lead to the same performance indicators, but during the optimization of process parameters, using current techniques, only one of these combinations can be…
Florian Privé
A few algorithms have been developed for splitting the genome in nearly independent blocks of linkage disequilibrium. Due to the complexity of this problem, these algorithms rely on heuristics, which makes them sub-optimal. Here we develop an optimal solution for this problem using dynamic programming. This is now…
Roman Joeres, David B. Blumenthal, Olga V. Kalinina
Information Leakage is an increasing problem in machine learning research. It is a common practice to report models with benchmarks, comparing them to the state-of-the-art performance on the test splits of datasets. If two or more dataset splits contain identical or highly similar samples, a model risks simply…
Kangbien Park, Yonghee Bae
Drift, selection, and mutation are integral evolutionary factors. In this article, operator model is newly suggested to intuitively represent those evolutionary factors into mathematical operators, and to ultimately offer unconventional methodology for understanding evolutionary dynamics. To be specific, each of the…
Authors not listed
Ongoing research involving electronic spin-dependent dynamics, such as chiral- induced spin selectivity, is providing impetus to revise our understanding of nuclear en- tanglement with electronic spatial and spin degrees of freedom. In a spin-independent setting, non-adiabatic couplings are well-known mediators of…