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An archived firefly algorithm; a mathematical software to solve univariate nonlinear equations

M. K. A. Ariyaratne, T. G. I. Fernando, S. Weerakoon
2016 The International Journal on Advances in ICT for Emerging Regions  
The modification; archived firefly algorithm [AFFA] exhibits the ability of finding almost all complex roots of a given nonlinear equation within a reasonable range.  ...  Computer simulations show that the AFFA performs well in solving nonlinear equations with real as well as complex roots within a specified region.  ...  As an improvement, we can test parameter optimization techniques which are able to adapt with our algorithm.  ... 
doi:10.4038/icter.v9i1.7169 fatcat:ze75wj2qgvfapb3yurtsw4dxqm

Interpreting Freeform Equation Solving [chapter]

Anna N. Rafferty, Thomas L. Griffiths
2015 Lecture Notes in Computer Science  
Hypothesizing that structured interfaces may frustrate some learners, we conducted an experiment comparing two interfaces for solving equations: one requires users to enter steps in an efficient sequence  ...  In order to make inferences from these more freeform data, we develop a Bayesian inverse planning algorithm for diagnosing algebra understanding that interprets individual equation solving steps and places  ...  Modeling Equation Solving To diagnose understanding from observations of solutions to linear equations, we developed a Bayesian inverse planning algorithm specifically for this domain, building on preliminary  ... 
doi:10.1007/978-3-319-19773-9_39 fatcat:32e4nscpmbex7jniadywhz5nqi

A Coupled Grid-Particle Method for Fluid Animation on GPU

Fengquan Zhang, Qiuming Wei, Zhaohui Wu
2020 Wireless Communications and Mobile Computing  
Furthermore, for achieving the real-time requirements of fluid animation, we use GPU parallel computing to accelerate the simulation and use an improved screen space fluid (SSF) rendering method for realistic  ...  Firstly, based on the nonequilibrium extrapolation method, we design a novel method for reconstructing distribution functions (DFs) of interface grids of lattice Boltzmann method (LBM) and couple the reconstruction  ...  The first solution to improve the accuracy of solving advection equation solution can only reduce but not avoid the error of solving the advection equation.  ... 
doi:10.1155/2020/8865931 fatcat:ksn2upfvm5f4njpwvo3xhvgcbe

Improved Fast Iterative Algorithm for Eikonal Equation for GPU Computing [article]

Yuhao Huang
2021 arXiv   pre-print
In this paper we propose an improved fast iterative method to solve the Eikonal equation, which can be implemented in parallel.  ...  We improve the fast iterative method for Eikonal equation in two novel ways, in the value update and in the error correction.  ...  The most time consuming part of the numerical method for the Eikonal equation is solving the quadratic equations (Algorithm 1).  ... 
arXiv:2106.15869v3 fatcat:a5s76ks6hrc3pdk6a7hgfm25qq

Recent Numerical and Algorithmic Advances within the Volume Tracking Framework for Modeling Interfacial Flows

Marianne M. François
2015 Procedia IUTAM  
In this paper, the multimaterial interface reconstruction method via power diagram, curvature estimation via heights and mean values and the balanced-force algorithm for surface tension are highlighted  ...  A review of recent advances made in numerical methods and algorithms within the volume tracking framework is presented.  ...  I would also like to thank the organizers of the IUTAM symposium for their invitation.  ... 
doi:10.1016/j.piutam.2015.04.037 fatcat:lho43lrdxbb7jkm25jvh3ope5e

Accurate and Robust Methods for Variable Density Incompressible Flows with Discontinuities [chapter]

W. J. Rider, D. B. Kothe, E. G. Puckett, I. D. Aleinov
1998 ICASE/LaRC Interdisciplinary Series in Science and Engineering  
Designing an efficient and scalable method for solving this system of linear equations is of paramount importance.  ...  Taking the divergence of (2) yields an elliptic equation for cp Once this equation is solved, the correction equation to the velocity is v u = v . avp. (3) u = u -a v p . d FRACTIONAL STEP METHODS AND  ... 
doi:10.1007/978-94-011-5169-6_11 fatcat:irmo7oefinbh3gz43jga4tlz6e

An Overset Grid Method for Fluid-Structure Interaction

Scott T. Miller, R. L. Campbell, C. W. Elsworth, J. S. Pitt, D. A. Boger
2014 World Journal of Mechanics  
An overset grid methodology is developed for the fully coupled analysis of fluid-structure interaction (FSI) problems.  ...  Our partitioned solution algorithm uses separate solvers for the fluid (finite volume method) and the structure (finite element method), with mesh motion computed only on a subset of component grids of  ...  Acknowledgements The authors would like to acknowledge support for this research from the Applied Research Laboratory at The Pennsylvania State University, especially the student support from the ARL Undergraduate  ... 
doi:10.4236/wjm.2014.47023 fatcat:5xe534ymfnbmlj6bjiwmdaxpwu

Improved Ultrasonic CT Imaging Algorithm of Concrete Structures Based on Simulated Annealing

Hengchang Jing
2014 Sensors & Transducers  
An improved simulated annealing (SA) algorithm based on chaos search and natural weight function is presented.  ...  annealing-backfire algorithm, and the CT image of structure is calculated and obtained by the algorithm.  ...  Acknowledgment This work was supported by Project 2007QN047 of Science Foundation of Henan University of Science and Technology.  ... 
doaj:41604e288ab742b8bd08e0a5194c53c8 fatcat:3soj6kwx5rhlxduttpx3aylfiu

Solving finite-element time-domain problems with GaBP

David Fernandez, Ali Akbarzadeh-Sharbaf, Warren J. Gross, Dennis Giannacopoulos
2016 2016 IEEE Conference on Electromagnetic Field Computation (CEFC)  
The CFM is a robust and versatile method most notable for its immersed treatment of interface problems of any geometry, to an arbitrary order of accuracy.  ...  Moreover, an in-depth analysis of the CFM algorithm is presented, in which performance bottlenecks are investigated and significant potential for parallelizability is identified.  ...  The CFM algorithm has the same steps regardless of the complexity of the problem being solved, with only the tiling and number of patches varying between different geometries and interface configurations  ... 
doi:10.1109/cefc.2016.7816127 fatcat:rqk4j3tfqrc3xavsfkgrgzogve

Convergent iterative schemes for time parallelization

Izaskun Garrido, Barry Lee, Gunnar E. Fladmark, Magne S. Espedal
2006 Mathematics of Computation  
In this paper, we present several such algorithms that actually exploit the sequential nature of time evolution through a predictorcorrector procedure.  ...  But for many evolutionary problems, computer simulation can benefit substantially from time parallelization methods.  ...  Improved parallel PC algorithm in Athena. We apply the improved parallel PC algorithm of Section 4.2 to the molar mass equations. 6.3.1. Computational results: Scalability.  ... 
doi:10.1090/s0025-5718-06-01832-1 fatcat:scpukglfwrfbdn5co4bzfk3adu

Volume of Fluid method for low-Mach-number compressible supercritical liquid jet

Jordi Poblador Ibanez, William Sirignano
2021 International Conference on Liquid Atomization and Spray Systems (ICLASS)  
are solved together at each interface cell; and c) phase-wise values for certain variables (e.g., velocity) are obtained via extrapolation techniques.  ...  The interface is tracked using a split Volume-of-Fluid method generalized for the case where the liquid velocity is not divergence-free and both phases exchange mass across the interface.  ...  The authors are also grateful for the support of the NSF grant with Award Number 1803833 and Dr. Ron Joslin as Scientific Officer.  ... 
doi:10.2218/iclass.2021.5914 fatcat:z2ndcl2wa5bcroyb3ssye2n7ea

Domain decomposition and parallel processing of a finite element model of the shallow water equations

I.M. Navon, Y. Cai
1993 Computer Methods in Applied Mechanics and Engineering  
We present nonoverlapping domain decomposition techniques applied to a two-stage Numerov-Galerkin finite element model of the shallow water equations over a limited-area domain.  ...  The resulting nonsymmetric Schur complement matrices, modified interface matrices as well as the subdomain coefficient matrices are solved using Preconditioned Conjugate Gradient Squared (PCGS) non-symmetric  ...  Acknowledgment The research of the second author is supported by the Air Force grant AFOSR-89-0462 through the Geophysical Fluid Dynamics Institute of the Florida State University and the DOE grant 120053223  ... 
doi:10.1016/0045-7825(93)90190-9 fatcat:vdmh4vzor5hyvf4gfhrn2fhb34

Level-Set Based Topology Optimization Using The Continuous Adjoint Method

Karpouzas, G.K.,, De Villiers, E.,
2017 Zenodo  
In the second step, the interface is evolved by solving a transport equation.  ...  In the first step, the surface sensitivity derivatives are extended towards the normal direction of the interface, by solving the velocity extension equation.  ...  The velocity of the interface is extended in a narrow band of cells by solving equation 6 for a few iterations.  ... 
doi:10.5281/zenodo.826215 fatcat:3cfmtyphnzfqbnmv7off7aosqy

An improved immersed finte element particle-in-cell method for plasma simulation [article]

Jinwei Bai and Yong Cao and Yuchuan Chu and Xu Zhang
2017 arXiv   pre-print
The combination of these two methods provides an effective tool for plasma simulation with complex interface/boundary.  ...  The immersed finite element (IFE) method is efficient for solving interface problems on Cartesian meshes, which is desirable for PIC method.  ...  Improved Algorithm for Force Deposit The potential distribution at grid points is obtained by solving linear algebraic equations contained in the immersed finite element method, and then for the electric  ... 
arXiv:1706.02827v1 fatcat:3g2utvv2xndmtffntnzidmkf5q

General approach for solving the density gradient theory in the interfacial tension calculations

Xiaodong Liang, Michael Locht Michelsen
2017 Fluid Phase Equilibria  
solve nonlinear algebraic equations.  ...  These findings naturally lead to a solution procedure that consists of an inner loop and an outer loop for calculating the interfacial tension of a planar interface.  ...  Kontogeorgis for many useful discussions. X. Liang wishes to thank Dr. Xingqing Xiao (NC State University, USA) for many useful comments.  ... 
doi:10.1016/j.fluid.2017.07.021 fatcat:mvo2k2ampbes7getzp3e4gksaa
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