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Computer Science, Interdisciplinary Applications
Linghua Kong, Yiyang Luo, Lan Wang, Meng Chen, Zhi Zhao
Summary: In this paper, the HOC-ADI method is applied to solve the 2D Ginzburg-Landau equation, with five numerical schemes proposed and compared through numerical experiments. The new numerical schemes are shown to be superior in terms of efficiency and accuracy.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
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Biology
Youssef Belhamadia, Zeinab Rammal
Summary: This study introduces three ADI schemes for efficient solution of the nonlinear cardiac monodomain model, aiming to reduce computational time and memory consumption. The proposed methods have second order accuracy and evaluate the ionic model only once per time-step. Large-scale two- and three-dimensional simulations show higher efficiency of the proposed methods.
COMPUTERS IN BIOLOGY AND MEDICINE
(2021)
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Mathematics, Applied
Yonghong Duan, Ruiping Wen
Summary: This paper proposes an alternating direction power method for computing the largest singular value and singular vector of a matrix. The method is similar to the power method but requires fewer operations in the iterations. Convergence of the new method is proven under suitable conditions. Theoretical analysis and numerical experiments demonstrate that the new method is feasible and more effective than the power method in certain cases.
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Mathematics, Applied
Min Zhang, Guo-Feng Zhang
Summary: In this work, an ADI scheme and a matrix splitting iteration method for solving 2D spatial fractional Ginzburg-Landau equations were proposed. The method demonstrated better performance in terms of iterative steps and computing time compared to existing iteration methods.
APPLIED MATHEMATICS LETTERS
(2021)
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Mathematics, Applied
Ying Wang, Fawang Liu, Liquan Mei, Vo V. Anh
Summary: In this paper, an efficient spectral Galerkin method for the three-dimensional multi-term time-space fractional diffusion equation is developed. The fully discrete numerical scheme is shown to be unconditionally stable, with second-order accuracy in time and optimal error estimation in space. The proposed method is validated through numerical experiments and applied to solve the fractional Bloch-Torrey model.
NUMERICAL ALGORITHMS
(2021)
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Mathematics, Applied
B. Kheirfam
Summary: In this paper, a new corrector-predictor interior-point method for solving semidefinite optimization is proposed. The centering equation of the system is transformed algebraically to define the central path. The algebraic transformation plays a crucial role in calculating the new search directions. The algorithm's iteration complexity is proven to match the best known results for interior-point methods (IPMs). This is the first corrector-predictor interior-point algorithm using search directions obtained from the desired algebraic transformation for semidefinite optimization. Numerical experiments are conducted to demonstrate the efficiency of the new algorithm.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
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Mathematics, Applied
Yue Wang, Hu Chen
Summary: The study focuses on using an alternating direction implicit (ADI) difference method to solve a two-dimensional time-fractional diffusion equation, discussing the temporal convergence and error estimation of the method, proving that the method has a certain accuracy globally.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
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Mathematics, Applied
Ali Ruhsen Cete, Oguz Kaan Onay
Summary: The study combines a novel fast-implicit iteration scheme called the alternating cell direction implicit (ACDI) method with the approximate factorization scheme to increase the accuracy of numerical solutions for partial differential equations. By applying the ACDI method to unstructured grids, the study shows improvement in the method's capabilities. The research results validate the enhancements brought by the ACDI method and demonstrate its potential for broader applications beyond structured grids.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2022)
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Mathematics, Applied
Xuehua Yang, Wenlin Qiu, Haixiang Zhang, Liang Tang
Summary: In this work, an efficient alternating direction implicit (ADI) finite difference scheme is proposed to solve the three-dimensional time-fractional telegraph equation. Stability and convergence of the scheme are proved via the energy method in L-2 and H-1 norms, and several numerical examples are provided to validate the theoretical results.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
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Mathematics, Applied
Qiong Huang, Ren-jun Qi, Wenlin Qiu
Summary: This study introduces an ADI Galerkin scheme for the nonlocal diffusion-wave equation in three-dimensional space, demonstrating its efficiency through numerical experiments.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
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Mathematics
Loic Beuken, Olivier Cheffert, Aleksandra Tutueva, Denis Butusov, Vincent Legat
Summary: This paper introduces new semi-explicit and semi-implicit predictor-corrector methods based on backward differentiation formula and Adams-Bashforth methods. The numerical stability and performance of these methods are thoroughly studied, and the results show the potential superiority of these methods in solving large-scale ODE systems.
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Mathematics, Applied
Mostafa Abbaszadeh, Mehdi Dehghan
Summary: The paper introduces a new high-order finite difference scheme with low computational complexity to solve the space-time fractional tempered diffusion equation. The stability analysis and convergence order proof demonstrate the effectiveness and feasibility of the technique.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2021)
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Computer Science, Theory & Methods
Grzegorz Gurgul, Bartosz Balis, Maciej Paszynski
Summary: This paper investigates the applications of computer simulations with isogeometric analysis (IGA), proposing a new algorithm for the IGA solver based on the Pregel computational model. The cloud-native solver implemented in the Apache Giraph framework demonstrates its effectiveness in solving challenging higher-order PDEs. The scalability of the proposed algorithm is evaluated in terms of various scalability models and run configurations.
FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE
(2023)
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Engineering, Electrical & Electronic
Peiyu Wu, Xin Wang, Yongjun Xie, Haolin Jiang, Toshiaki Natsuki
Summary: This study proposes an improved algorithm to enhance the stability and accuracy of the explicit finite-difference time-domain (FDTD) algorithm. By combining the complex envelope method and alternating direction implicit method, the bandpass simulation is achieved and the time increment problem within implicit schemes is solved. The proposed scheme demonstrates good absorption and efficiency in the simulation and can be extensively applied to various types of materials.
IEEE TRANSACTIONS ON MAGNETICS
(2022)
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Mathematics, Applied
M. Rakhuba
Summary: This paper introduces a robust numerical solver for efficiently solving a three-dimensional elliptic problem in a data-sparse quantized tensor format, using the TQTT format. The utilization of the alternating direction implicit method helps to avoid numerical instabilities caused by differential operators.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
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Computer Science, Software Engineering
Hadi Khatibzadeh, Ali Shokri
OPTIMIZATION METHODS & SOFTWARE
(2015)
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Mathematics, Applied
Ali Shokri, Ali Habibirad
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2016)
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Engineering, Multidisciplinary
Ali Shokri, Erfan Bahmani
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2019)
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Computer Science, Interdisciplinary Applications
Ali Shokri, Mehdi Dehghan
COMPUTER PHYSICS COMMUNICATIONS
(2010)
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Mathematics, Applied
Mehdi Dehghan, Ali Shokri
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2009)
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Computer Science, Interdisciplinary Applications
Mehdi Dehghan, Ali Shokri
MATHEMATICS AND COMPUTERS IN SIMULATION
(2008)
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Mathematics, Applied
Mehdi Dehghan, Ali Shokri
NUMERICAL ALGORITHMS
(2009)
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Mathematics, Applied
M. Dehghan, Ali Shokri
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2008)
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Mathematics, Applied
Mehdi Dehghan, Ali Shokri
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2008)
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Mathematics, Applied
Ali Shokri, Mehdi Dehghan
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2010)
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Mathematics, Applied
Mehdi Dehghan, Ali Shokri
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2009)
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Engineering, Multidisciplinary
Ali Shokri, Mehdi Dehghan
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2012)
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Engineering, Mechanical
Mehdi Dehghan, Ali Shokri
NONLINEAR DYNAMICS
(2007)
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Mathematics, Applied
Mehdi Dehghan, Ali Shokri
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2007)
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Computer Science, Interdisciplinary Applications
Usman Riaz, E. Seegyoung Seol, Robert Hager, Mark S. Shephard
Summary: The accurate representation and effective discretization of a problem domain into a mesh are crucial for achieving high-quality simulation results and computational efficiency. This work presents recent developments in extending an automated tokamak modeling and meshing infrastructure to better support the near flux field following meshing requirements of the XGC Gyro-kinetic Code.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Zhenglu Li, Gabriel Antonius, Yang-Hao Chan, Steven G. Louie
Summary: This article presents a workflow for practical calculations of electron-phonon coupling and includes the effect of many-electron correlations using GW perturbation theory. The workflow combines different software packages to enable accurate calculations at the level of quasiparticle band structures.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Akihiro Koide, Sara Rabouli, Pierre Le Meur, Sylvain Tricot, Philippe Schieffer, Didier Sebilleau, Calogero R. Natoli
Summary: We present the MsSpec Atomic Scattering Amplitude Package (MASAP), which includes a computation program and a graphical interface for generating atomic scattering amplitude (ASA). The study investigates the applicability of plane wave (PW) and curved spherical wave (SW) scattering in describing electron propagation. The results show that the imaginary part of the optical potential enhances the elastic scattering in the forward direction but causes damping effects in other directions.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
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Computer Science, Interdisciplinary Applications
A. Bagci, Gustavo A. Aucar
Summary: The electron repulsion integrals over Slater-type orbitals with non-integer principal quantum numbers are investigated in this study. These integrals are important in calculations of many-electron systems. New relationships free from hyper-geometric functions are derived to simplify the calculations. With the use of auxiliary functions and straightforward recurrence relationships, these integrals can be efficiently computed, providing initial conditions for the evaluation of expectation values and potentials.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
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Computer Science, Interdisciplinary Applications
Andrzej Daniluk
Summary: RHEED_DIFF_2D is an open-source software for qualitative numerical simulations of RHEED oscillation intensity changes with layer deposition, used for interpreting heteroepitaxial structures under different scattering crystal potential models.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
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Computer Science, Interdisciplinary Applications
Niklas Kuehl, Hendrik Fischer, Michael Hinze, Thomas Rung
Summary: The article presents a strategy and algorithm for simulation-accompanying, incremental Singular Value Decomposition (SVD) for time-evolving, spatially parallel discrete data sets. The proposed method improves computational efficiency by introducing a bunch matrix, resulting in higher accuracy and practical applicability.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jose M. Rodriguez-Borbon, Xian Wang, Adrian P. Dieguez, Khaled Z. Ibrahim, Bryan M. Wong
Summary: This paper presents an open-source software package called TRAVOLTA for massively parallelized quantum optimal control calculations on GPUs. The TRAVOLTA package is an improvement on the previous NIC-CAGE algorithm and incorporates algorithmic improvements for faster convergence. Three different variants of GPU parallelization are examined to evaluate their performance in constructing optimal control fields in various quantum systems. The benchmarks show that the GPU-enhanced TRAVOLTA code produces the same results as previous CPU-based algorithms but with a speedup of more than ten times. The GPU enhancements and algorithmic improvements allow large quantum optimal control calculations to be efficiently executed on modern multi-core computational hardware.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Weijie Hua
Summary: This work introduces a program called MCNOX for computing and analyzing ultrafast nonlinear X-ray spectra. It is designed for cutting-edge applications in photochemistry/photophysics enabled by X-ray free-electron lasers and high harmonic generation light sources. The program can calculate steady-state X-ray absorption spectroscopy and three types of ultrafast nonlinear X-ray spectra, and it is capable of identifying major electronic transitions and providing physical and chemical insights from complex signals.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Leandro Benatto, Omar Mesquita, Lucimara S. Roman, Rodrigo B. Capaz, Graziani Candiotto, Marlus Koehler
Summary: Photoluminescence Quenching Simulator (PLQ-Sim) is a user-friendly software for studying the dynamics of photoexcited states at the interface between organic semiconductors. It provides important information on organic photovoltaic and photothermal devices and calculates transfer rates and quenching efficiency.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Dongming Li, James Kestyn, Eric Polizzi
Summary: This study introduces a practical and efficient approach to calculate the all-electron full potential band structure in real space using a finite element basis. Instead of the k-space method, this method solves the Kohn-Sham equation self-consistently within a larger finite system enclosing the unit-cell. Non-self-consistent calculations are then performed in the Brillouin zone to obtain the band structure results, which are found to be in excellent agreement with the pseudopotential k-space method. Furthermore, the study successfully observes the band bending of core electrons.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
R. Kleiber, M. Borchardt, R. Hatzky, A. Koenies, H. Leyh, A. Mishchenko, J. Riemann, C. Slaby, J. M. Garcia-Regana, E. Sanchez, M. Cole
Summary: This paper describes the current state of the EUTERPE code, focusing on the implemented models and their numerical implementation. The code is capable of solving the multi-species electromagnetic gyrokinetic equations in a three-dimensional domain. It utilizes noise reduction techniques and grid resolution transformation for efficient computation. Additionally, various hybrid models are implemented for comparison and the study of plasma-particle interactions. The code is parallelized for high scalability on multiple CPUs.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Pengliang Yang
Summary: This paper presents an open source software called SMIwiz, which combines seismic modelling, reverse time migration, and full waveform inversion into a unified computer implementation. SMIwiz supports both 2D and 3D simulations and provides various computational recipes for efficient calculation. Its independent processing and batchwise job scheduling ensure scalability, and its viability is demonstrated through applications on benchmark models.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Christian Tantardini, Miroslav Ilias, Matteo Giantomassi, Alexander G. Kvashnin, Valeria Pershina, Xavier Gonze
Summary: Material discovery has been an active research field, and this study focuses on developing pseudopotentials for actinides and super-heavy elements. These pseudopotentials are crucial for accurate first-principles calculations and simulations.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
S. Blanes, F. Casas, C. Gonzalez, M. Thalhammer
Summary: This paper explores the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. Numerical experiments confirm the advantages of the proposed fourth-order modified operator splitting method over traditional splitting methods in dealing with Gross-Pitaevskii systems.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Siegfried Kaidisch, Thomas U. Hilger, Andreas Krassnigg, Wolfgang Lucha
Summary: Motivated by a use case in theoretical hadron physics, this paper revisits an application of a pole-sum fit to dressing functions of a confined quark propagator. Specifically, it investigates approaches to determine the number and positions of singularities closest to the origin for a function known numerically on a specific grid on the positive real axis. Comparing the efficiency of standard techniques to a pure artificial-neural-network approach and a combination of both, it finds that the combined approach is more efficient. This approach can be applied to similar situations where the positions of poles need to be estimated quickly and reliably from real-axis information alone.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
