Using Space Mapping and Surrogate Models to Optimize Vehicle Crashworthiness Design

Redhe, Marcus; Nilsson, Larsgunnar

doi:10.2514/6.2002-5536

Cited by 41 publications

(26 citation statements)

References 5 publications

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“…The space-mapping technique has been mainly applied in electromagnetics [6,8] but, since the underlying principles are quite general, it could also be used in other areas [22,27]. Space mapping has developed enormously during the last decade.…”

Section: Introductionmentioning

confidence: 99%

Space Mapping and Defect Correction

Echeverria

Hemker

2005

Comput. Methods Appl. Math.

120

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-In this paper we show that space-mapping optimization can be understood in the framework of defect correction. Then, space-mapping algorithms can be seen as special cases of defect correction iteration. In order to analyze the properties of space mapping and the space-mapping function, we introduce the new concept of flexibility of the underlying models. The best space-mapping results are obtained for so-called equally flexible models. By introducing an affine operator as a left preconditioner, two models can be made equally flexible, at least in the neighborhood of a solution. This motivates an improved space-mapping (or manifold-mapping) algorithm. The left preconditioner complements traditional space mapping where only a right preconditioner is used. In the last section a few simple examples illustrate some of the phenomena analyzed in this paper.2000 Mathematics Subject Classification: 65K05; 65B05.

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Section: Introductionmentioning

confidence: 99%

Space Mapping and Defect Correction

Echeverria

Hemker

2005

Comput. Methods Appl. Math.

120

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“…Step 1; else terminate the algorithm: (14) Note that the adaptive algorithm (14) does not require any extra fine model evaluations because the coarse model assessment is based on already existing fine model data. Additional computational effort concerns the coarse model only, and because we assume that the coarse model evaluation is significantly cheaper than the fine model evaluation, this additional effort should not substantially affect the total execution time of the optimisation algorithm.…”

Section: Coarse Models and Preassigned Parametersmentioning

confidence: 99%

Implicit space mapping with adaptive selection of preassigned parameters

Koziel

Cheng

Bandler

2010

IET Microw. Antennas Propag.

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“…The space-mapping technique has been mainly applied in electromagnetics [6,8] but, since the underlying principles are quite general, it could also be used in other areas [23,28]. Space mapping has developed enormously during the last decade.…”

Section: Introductionmentioning

confidence: 99%

“…As an example, in Section 5.2 we significantly accelerate the solution process for an optimization problem from magnetostatics by combining finite elements for the precise computations of the magnetic field with rather simple magnetic circuit calculations. The space-mapping technique has been mainly applied in electromagnetics [6,8] but, since the underlying principles are quite general, it could also be used in other areas [23,28]. Space mapping has developed enormously during the last decade.…”

mentioning

confidence: 99%

Space Mapping and Defect Correction

Echeverria

Lahaye

Hemker

2008

Mathematics in Industry

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C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a MAS Modelling, Analysis and Simulation Modelling, Analysis and SimulationSpace mapping and defect correction D. Echeverría, P.W. Hemker Space mapping and defect correction ABSTRACT In this paper we show that space-mapping optimization can be understood in the framework of defect correction. Then, space-mapping algorithms can be seen as special cases of defect correction iteration. In order to analyze properties of space mapping and the space-mapping function we introduce the new concept of flexibility of the underlying models. The best spacemapping results are obtained for so-called equally flexible models. By introducing an affine operator as a left preconditioner, two models can be made equally flexible, at least in the neighborhood of a solution. This motivates an improved space-mapping (or manifold-mapping) algorithm. The left preconditioner complements traditional space mapping where only a right preconditioner is used. In the last section a few simple examples illustrate some of the phenomena analyzed in this paper. REPORT MAS-E0506 MARCH 2005 ABSTRACTIn this paper we show that space-mapping optimization can be understood in the framework of defect correction. Then, space-mapping algorithms can be seen as special cases of defect correction iteration. In order to analyze properties of space mapping and the space-mapping function we introduce the new concept of flexibility of the underlying models. The best space-mapping results are obtained for so-called equally flexible models.By introducing an affine operator as a left preconditioner, two models can be made equally flexible, at least in the neighborhood of a solution. This motivates an improved space-mapping (or manifold-mapping) algorithm. The left preconditioner complements traditional space mapping where only a right preconditioner is used. In the last section a few simple examples illustrate some of the phenomena analyzed in this paper. Mathematics Subject Classification: 65K05, 65B05Keywords and Phrases: Space mapping, defect correction, two-level optimization IntroductionThe space-mapping idea was conceived by Bandler [4] in the field of microwave filter design. It aims at reducing the cost of accurate optimization computations by iteratively correcting a sequence of rougher approximations. In technological applications this allows us to couple simple rules that represent expert knowledge accumulated over the years with the accuracy of expensive simulation techniques based on the numerical solution of partial differential equations. This combination may yield an efficient method with good accuracy of the final solution. As an example, in Section 5.2 we significantly accelerate the solution process for an optimization problem from magnetostatics by combining finite elements for the precise computations of the magnetic field with rather simple magnetic circuit calculations. The space-mapping technique has been mainly applied in electromagnetics [6,8] but, since the underlying principles...

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Using Space Mapping and Surrogate Models to Optimize Vehicle Crashworthiness Design

Cited by 41 publications

References 5 publications

Space Mapping and Defect Correction

Space Mapping and Defect Correction

Implicit space mapping with adaptive selection of preassigned parameters

Space Mapping and Defect Correction

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