Finite Volumes Discretization of Topology Optimization Problems

Publication: Research - peer-reviewConference abstract for conference – Annual report year: 2011

Standard

Finite Volumes Discretization of Topology Optimization Problems. / Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter.

2011. Abstract from US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, .

Publication: Research - peer-reviewConference abstract for conference – Annual report year: 2011

Harvard

Evgrafov, A, Gregersen, MM & Sørensen, MP 2011, 'Finite Volumes Discretization of Topology Optimization Problems' US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, 01/01/11,

APA

Evgrafov, A., Gregersen, M. M., & Sørensen, M. P. (2011). Finite Volumes Discretization of Topology Optimization Problems. Abstract from US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, .

CBE

Evgrafov A, Gregersen MM, Sørensen MP. 2011. Finite Volumes Discretization of Topology Optimization Problems. Abstract from US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, .

MLA

Vancouver

Evgrafov A, Gregersen MM, Sørensen MP. Finite Volumes Discretization of Topology Optimization Problems. 2011. Abstract from US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, .

Author

Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter / Finite Volumes Discretization of Topology Optimization Problems.

2011. Abstract from US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, .

Publication: Research - peer-reviewConference abstract for conference – Annual report year: 2011

Bibtex

@misc{7f2348a2e9034d9ebdf550f3609b2b82,
title = "Finite Volumes Discretization of Topology Optimization Problems",
author = "Anton Evgrafov and Gregersen, {Misha Marie} and Sørensen, {Mads Peter}",
year = "2011",
type = "ConferencePaper <importModel: ConferenceImportModel>",

}

RIS

TY - ABST

T1 - Finite Volumes Discretization of Topology Optimization Problems

A1 - Evgrafov,Anton

A1 - Gregersen,Misha Marie

A1 - Sørensen,Mads Peter

AU - Evgrafov,Anton

AU - Gregersen,Misha Marie

AU - Sørensen,Mads Peter

PY - 2011

Y1 - 2011

N2 - Utilizing control in the coecients of partial dierential equations (PDEs) for the purpose of optimal design, or topology optimization, is a well established technique in both academia and industry. Advantages of using control in the coecients for optimal design purposes include the exibility of the induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout the optimization procedure. As topology optimization is gaining maturity, the method is applied to increasingly more complex coupled multi-physical problems. As a result it becomes vital to utilize robust and mature PDE solvers within a topology optimization framework. Finite volume methods (FVMs) represent such a mature and versatile technique for discretiz- ing partial dierential equations in the form of conservation laws of varying types. Advantages of FVMs include the simplicity of implementation, their local conservation properties, and the ease of coupling various PDEs in a multi-physics setting. In fact, FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly attractive, as all involved PDEs on a given domain are discretized using the same and the low- est possible number of degrees of freedom. In spite of their numerous favourable advantages, FVMs have seen very little adoption within the topology optimization community, where the absolute majority of numerical computations is done using nite element methods (FEMs). Despite some limited recent eorts [1, 2], we have only started to develop our understanding of the interplay between the control in the coecients and FVMs. Recent advances in discrete functional analysis allow us to analyze convergence of FVM discretizations of model topology optimization problems. We illustrate the numerical behaviour of a cell based FVM topology optimization algorithm on a series of benchmark examples.

AB - Utilizing control in the coecients of partial dierential equations (PDEs) for the purpose of optimal design, or topology optimization, is a well established technique in both academia and industry. Advantages of using control in the coecients for optimal design purposes include the exibility of the induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout the optimization procedure. As topology optimization is gaining maturity, the method is applied to increasingly more complex coupled multi-physical problems. As a result it becomes vital to utilize robust and mature PDE solvers within a topology optimization framework. Finite volume methods (FVMs) represent such a mature and versatile technique for discretiz- ing partial dierential equations in the form of conservation laws of varying types. Advantages of FVMs include the simplicity of implementation, their local conservation properties, and the ease of coupling various PDEs in a multi-physics setting. In fact, FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly attractive, as all involved PDEs on a given domain are discretized using the same and the low- est possible number of degrees of freedom. In spite of their numerous favourable advantages, FVMs have seen very little adoption within the topology optimization community, where the absolute majority of numerical computations is done using nite element methods (FEMs). Despite some limited recent eorts [1, 2], we have only started to develop our understanding of the interplay between the control in the coecients and FVMs. Recent advances in discrete functional analysis allow us to analyze convergence of FVM discretizations of model topology optimization problems. We illustrate the numerical behaviour of a cell based FVM topology optimization algorithm on a series of benchmark examples.

UR - http://www.usnccm.org/

ER -