skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Automatic Black-Box Model Order Reduction using Radial Basis Functions

Abstract

Finite elements methods have long made use of model order reduction (MOR), particularly in the context of fast freqeucny sweeps. In this paper, we discuss a black-box MOR technique, applicable to a many solution methods and not restricted only to spectral responses. We also discuss automated methods for generating a reduced order model that meets a given error tolerance. Numerical examples demonstrate the effectiveness and wide applicability of the method. With the advent of improved computing hardware and numerous fast solution techniques, the field of computational electromagnetics are progressed rapidly in terms of the size and complexity of problems that can be solved. Numerous applications, however, require the solution of a problem for many different configurations, including optimization, parameter exploration, and uncertainly quantification, where the parameters that may be changed include frequency, material properties, geometric dimensions, etc. In such cases, thousands of solutions may be needed, so solve times of even a few minutes can be burdensome. Model order reduction (MOR) may alleviate this difficulty by creating a small model that can be evaluated quickly. Many MOR techniques have been applied to electromagnetic problems over the past few decades, particularly in the context of fast frequency sweeps. Recent works havemore » extended these methods to allow more than one parameter and to allow the parameters to represent material and geometric properties. There are still limitations with these methods, however. First, they almost always assume that the finite element method is used to solve the problem, so that the system matrix is a known function of the parameters. Second, although some authors have presented adaptive methods (e.g., [2]), the order of the model is often determined before the MOR process begins, with little insight about what order is actually needed to reach the desired accuracy. Finally, it not clear how to efficiently extend most methods to the multiparameter case. This paper address the above shortcomings be developing a method that uses a block-box approach to the solution method, is adaptive, and is easily extensible to many parameters.« less

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1022934
Report Number(s):
LLNL-CONF-491136
TRN: US201118%%610
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Conference
Resource Relation:
Conference: Presented at: IEEE Antennas and Propagation Society, Spokane, WA, United States, Jul 04 - Jul 08, 2001
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; ACCURACY; ANTENNAS; DIMENSIONS; EXPLORATION; FINITE ELEMENT METHOD; OPTIMIZATION; SPECTRAL RESPONSE; TOLERANCE

Citation Formats

Stephanson, M B, Lee, J F, and White, D A. Automatic Black-Box Model Order Reduction using Radial Basis Functions. United States: N. p., 2011. Web.
Stephanson, M B, Lee, J F, & White, D A. Automatic Black-Box Model Order Reduction using Radial Basis Functions. United States.
Stephanson, M B, Lee, J F, and White, D A. Fri . "Automatic Black-Box Model Order Reduction using Radial Basis Functions". United States. https://www.osti.gov/servlets/purl/1022934.
@article{osti_1022934,
title = {Automatic Black-Box Model Order Reduction using Radial Basis Functions},
author = {Stephanson, M B and Lee, J F and White, D A},
abstractNote = {Finite elements methods have long made use of model order reduction (MOR), particularly in the context of fast freqeucny sweeps. In this paper, we discuss a black-box MOR technique, applicable to a many solution methods and not restricted only to spectral responses. We also discuss automated methods for generating a reduced order model that meets a given error tolerance. Numerical examples demonstrate the effectiveness and wide applicability of the method. With the advent of improved computing hardware and numerous fast solution techniques, the field of computational electromagnetics are progressed rapidly in terms of the size and complexity of problems that can be solved. Numerous applications, however, require the solution of a problem for many different configurations, including optimization, parameter exploration, and uncertainly quantification, where the parameters that may be changed include frequency, material properties, geometric dimensions, etc. In such cases, thousands of solutions may be needed, so solve times of even a few minutes can be burdensome. Model order reduction (MOR) may alleviate this difficulty by creating a small model that can be evaluated quickly. Many MOR techniques have been applied to electromagnetic problems over the past few decades, particularly in the context of fast frequency sweeps. Recent works have extended these methods to allow more than one parameter and to allow the parameters to represent material and geometric properties. There are still limitations with these methods, however. First, they almost always assume that the finite element method is used to solve the problem, so that the system matrix is a known function of the parameters. Second, although some authors have presented adaptive methods (e.g., [2]), the order of the model is often determined before the MOR process begins, with little insight about what order is actually needed to reach the desired accuracy. Finally, it not clear how to efficiently extend most methods to the multiparameter case. This paper address the above shortcomings be developing a method that uses a block-box approach to the solution method, is adaptive, and is easily extensible to many parameters.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2011},
month = {7}
}

Conference:
Other availability
Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that hold this conference proceeding.

Save / Share: