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Algorithm 860: SimpleS—an extension of Freudenthal's simplex subdivision

Authors:

Eduardo N. Gonçalves,

Reinaldo M. Palhares,

Ricardo H. C. Takahashi,

Renato C. MesquitaAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 32, Issue 4

Pages 609 - 621

https://doi.org/10.1145/1186785.1186792

Published: 01 December 2006 Publication History

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Abstract

This article presents a simple efficient algorithm for the subdivision of a d-dimensional simplex in k^d simplices, where k is any positive integer number. The algorithm is an extension of Freudenthal's subdivision method. The proposed algorithm deals with the more general case of k^d subdivision, and is considerably simpler than the RedRefinementND algorithm for implementation of Freudenthal's strategy. The proposed simplex subdivision algorithm is motivated by a problem in the field of robust control theory: the computation of a tight upper bound of a dynamical system performance index by means of a branch-and-bound algorithm.

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References

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Cited By

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Souza AOliveira RPeres P(2024) Computation of stable convex combinations of a set of matrices through LMIs with application in control of switched linear systems Systems & Control Letters10.1016/j.sysconle.2024.105833189(105833)Online publication date: Jul-2024
https://doi.org/10.1016/j.sysconle.2024.105833
Gonçalves EOliveira Pda Silva Júnior J(2023) ℋ ∞ robust control of discrete‐time systems based on new linear matrix inequality formulations and evolutionary optimization Optimal Control Applications and Methods10.1002/oca.308745:3(1045-1063)Online publication date: 27-Nov-2023
https://doi.org/10.1002/oca.3087
Petrov MTodorov T(2019)Refinement strategies related to cubic tetrahedral meshesApplied Numerical Mathematics10.1016/j.apnum.2018.11.006137(169-183)Online publication date: Mar-2019
https://doi.org/10.1016/j.apnum.2018.11.006
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Index Terms

Algorithm 860: SimpleS—an extension of Freudenthal's simplex subdivision
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 32, Issue 4

December 2006

145 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/1186785

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 December 2006

Published in TOMS Volume 32, Issue 4

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Cited By

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Souza AOliveira RPeres P(2024) Computation of stable convex combinations of a set of matrices through LMIs with application in control of switched linear systems Systems & Control Letters10.1016/j.sysconle.2024.105833189(105833)Online publication date: Jul-2024
https://doi.org/10.1016/j.sysconle.2024.105833
Gonçalves EOliveira Pda Silva Júnior J(2023) ℋ ∞ robust control of discrete‐time systems based on new linear matrix inequality formulations and evolutionary optimization Optimal Control Applications and Methods10.1002/oca.308745:3(1045-1063)Online publication date: 27-Nov-2023
https://doi.org/10.1002/oca.3087
Petrov MTodorov T(2019)Refinement strategies related to cubic tetrahedral meshesApplied Numerical Mathematics10.1016/j.apnum.2018.11.006137(169-183)Online publication date: Mar-2019
https://doi.org/10.1016/j.apnum.2018.11.006
Bachur WGonalves ERamrez JBatista L(2017)A multiobjective robust controller synthesis approach aided by multicriteria decision analysisApplied Soft Computing10.1016/j.asoc.2017.06.02760:C(374-386)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1016/j.asoc.2017.06.027
Xuan ZPapadopoulos P(2016)Computing an upper bound on contact stress with surrogate dualityComputational Mechanics10.1007/s00466-016-1287-x58:1(171-183)Online publication date: 1-Jul-2016
https://dl.acm.org/doi/10.1007/s00466-016-1287-x
Siqueira MSilva LGoncalves EPalhares RTakahashi R(2014)Robust decoupling control synthesis2014 American Control Conference10.1109/ACC.2014.6858972(4280-4285)Online publication date: Jun-2014
https://doi.org/10.1109/ACC.2014.6858972
Paulavičius RŽilinskas JPaulavičius RŽilinskas J(2013)Simplicial Partitions in Global OptimizationSimplicial Global Optimization10.1007/978-1-4614-9093-7_1(1-19)Online publication date: 15-Sep-2013
https://doi.org/10.1007/978-1-4614-9093-7_1
Gonçalves BGonçalves EPalhares RTakahashi R(2012)Robust decoupling PI controllers for multi-loop control2012 IEEE 51st IEEE Conference on Decision and Control (CDC)10.1109/CDC.2012.6426606(1530-1535)Online publication date: Dec-2012
https://doi.org/10.1109/CDC.2012.6426606
Neumüller MSteinbach O(2012)Refinement of flexible space–time finite element meshes and discontinuous Galerkin methodsComputing and Visualization in Science10.1007/s00791-012-0174-z14:5(189-205)Online publication date: 18-Apr-2012
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Gonçalves EBachur WPalhares RTakahashi R(2011) Robust ℋ 2 /ℋ ∞ /reference model dynamic output-feedback control synthesis International Journal of Control10.1080/00207179.2011.63323284:12(2067-2080)Online publication date: Dec-2011
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