Comparison between Material Point Method and meshfree schemes derived from optimal transportation theory

Lisa Wobbes; Roel Tielen; Matthias Möller; Kees Vuik; Vahid Galavi

Comparison between Material Point Method and meshfree schemes derived from optimal transportation theory

Lisa Wobbes, Roel Tielen, Matthias Möller, Kees Vuik, Vahid Galavi

Numerical Analysis

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

Both the Material Point Method (MPM) and meshfree schemes based on optimal transport theory have been developed for efficient and robust integration of the weak form equations originating from computational mechanics. Although the methods are derived in a different fashion, their algorithms share many similarities. In this paper, we outline the close resemblance of MPM and Optimal Transportation Meshfree (OTM) schemes. Aside from a theoretical analysis, the methods are compared numerically using a one-dimensionalbenchmark.

Original language	English
Title of host publication	Proceedings of the Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction
Subtitle of host publication	8 – 10 January 2019, University of Cambridge, United Kingdom
Pages	173-178
Number of pages	6
Publication status	Published - 2019
Event	MPM 2019: 2nd International Conference on the Material Point Method for Modelling Soil–Water–Structure Interaction - Cambridge, United Kingdom Duration: 8 Jan 2019 → 10 Jan 2019 Conference number: 2 http://mpm2019.eu/home

Conference

Conference	MPM 2019: 2nd International Conference on the Material Point Method for Modelling Soil–Water–Structure Interaction
Abbreviated title	MPM 2019
Country/Territory	United Kingdom
City	Cambridge
Period	8/01/19 → 10/01/19
Internet address	http://mpm2019.eu/home

Bibliographical note

green

Keywords

Material Point Method
Optimal Transportation Theory
Meshfree Methods

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Wobbes, L., Tielen, R., Möller, M., Vuik, K., & Galavi, V. (2019). Comparison between Material Point Method and meshfree schemes derived from optimal transportation theory. In Proceedings of the Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction: 8 – 10 January 2019, University of Cambridge, United Kingdom (pp. 173-178). Article mpm2019.28 http://mpm2019.eu/papers

Wobbes, Lisa ; Tielen, Roel ; Möller, Matthias et al. / Comparison between Material Point Method and meshfree schemes derived from optimal transportation theory. Proceedings of the Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction: 8 – 10 January 2019, University of Cambridge, United Kingdom. 2019. pp. 173-178

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title = "Comparison between Material Point Method and meshfree schemes derived from optimal transportation theory",

abstract = "Both the Material Point Method (MPM) and meshfree schemes based on optimal transport theory have been developed for efficient and robust integration of the weak form equations originating from computational mechanics. Although the methods are derived in a different fashion, their algorithms share many similarities. In this paper, we outline the close resemblance of MPM and Optimal Transportation Meshfree (OTM) schemes. Aside from a theoretical analysis, the methods are compared numerically using a one-dimensionalbenchmark.",

keywords = "Material Point Method, Optimal Transportation Theory, Meshfree Methods",

author = "Lisa Wobbes and Roel Tielen and Matthias M{\"o}ller and Kees Vuik and Vahid Galavi",

note = "green; MPM 2019: 2nd International Conference on the Material Point Method for Modelling Soil–Water–Structure Interaction, MPM 2019 ; Conference date: 08-01-2019 Through 10-01-2019",

year = "2019",

language = "English",

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Wobbes, L, Tielen, R, Möller, M , Vuik, K & Galavi, V 2019, Comparison between Material Point Method and meshfree schemes derived from optimal transportation theory. in Proceedings of the Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction: 8 – 10 January 2019, University of Cambridge, United Kingdom., mpm2019.28, pp. 173-178, MPM 2019: 2nd International Conference on the Material Point Method for Modelling Soil–Water–Structure Interaction, Cambridge, United Kingdom, 8/01/19. <http://mpm2019.eu/papers>

Comparison between Material Point Method and meshfree schemes derived from optimal transportation theory. / Wobbes, Lisa; Tielen, Roel; Möller, Matthias et al.
Proceedings of the Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction: 8 – 10 January 2019, University of Cambridge, United Kingdom. 2019. p. 173-178 mpm2019.28.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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AU - Galavi, Vahid

N1 - Conference code: 2

PY - 2019

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N2 - Both the Material Point Method (MPM) and meshfree schemes based on optimal transport theory have been developed for efficient and robust integration of the weak form equations originating from computational mechanics. Although the methods are derived in a different fashion, their algorithms share many similarities. In this paper, we outline the close resemblance of MPM and Optimal Transportation Meshfree (OTM) schemes. Aside from a theoretical analysis, the methods are compared numerically using a one-dimensionalbenchmark.

AB - Both the Material Point Method (MPM) and meshfree schemes based on optimal transport theory have been developed for efficient and robust integration of the weak form equations originating from computational mechanics. Although the methods are derived in a different fashion, their algorithms share many similarities. In this paper, we outline the close resemblance of MPM and Optimal Transportation Meshfree (OTM) schemes. Aside from a theoretical analysis, the methods are compared numerically using a one-dimensionalbenchmark.

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M3 - Conference contribution

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BT - Proceedings of the Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction

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Wobbes L, Tielen R, Möller M , Vuik K, Galavi V. Comparison between Material Point Method and meshfree schemes derived from optimal transportation theory. In Proceedings of the Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction: 8 – 10 January 2019, University of Cambridge, United Kingdom. 2019. p. 173-178. mpm2019.28

Comparison between Material Point Method and meshfree schemes derived from optimal transportation theory

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Keywords

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