scholarly journals Model-order reduction of electromagnetic fields in open domains

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. WB61-WB70
Author(s):  
Jörn Zimmerling ◽  
Vladimir Druskin ◽  
Mikhail Zaslavsky ◽  
Rob F. Remis
Keyword(s):  
Model Order Reduction ◽  
Maxwell Equations ◽  
Order Reduction ◽  
Efficient Computation ◽  
Scattering Problems ◽  
Model Order ◽  
Reduced Order ◽  
Advantages And Disadvantages ◽  
Reduction Techniques ◽  
Memory Efficient

We have developed several Krylov projection-based model-order reduction techniques to simulate electromagnetic wave propagation and diffusion in unbounded domains. Such techniques can be used to efficiently approximate transfer function field responses between a given set of sources and receivers and allow for fast and memory-efficient computation of Jacobians, thereby lowering the computational burden associated with inverse scattering problems. We found how general wavefield principles such as reciprocity, passivity, and the Schwarz reflection principle translate from the analytical to the numerical domain and developed polynomial, extended, and rational Krylov model-order reduction techniques that preserve these structures. Furthermore, we found that the symmetry of the Maxwell equations allows for projection onto polynomial and extended Krylov subspaces without saving a complete basis. In particular, short-term recurrence relations can be used to construct reduced-order models that are as memory efficient as time-stepping algorithms. In addition, we evaluated the differences between Krylov reduced-order methods for the full wave and diffusive Maxwell equations and we developed numerical examples to highlight the advantages and disadvantages of the discussed methods.

Trimming a Hazard Logic Tree with a New Model-Order-Reduction Technique

2017 ◽  
Vol 33 (3) ◽  
pp. 857-874 ◽  
Author(s):  
Keith Porter ◽  
Edward Field ◽  
Kevin Milner
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Computational Effort ◽  
Logic Tree ◽  
Model Order ◽  
New Approach ◽  
Reduced Order ◽  
Reduction Techniques ◽  
Possibility Space ◽  
Diagram Approach

The size of the logic tree within the Uniform California Earthquake Rupture Forecast Version 3, Time-Dependent (UCERF3-TD) model can challenge risk analyses of large portfolios. An insurer or catastrophe risk modeler concerned with losses to a California portfolio might have to evaluate a portfolio 57,600 times to estimate risk in light of the hazard possibility space. Which branches of the logic tree matter most, and which can one ignore? We employed two model-order-reduction techniques to simplify the model. We sought a subset of parameters that must vary, and the specific fixed values for the remaining parameters, to produce approximately the same loss distribution as the original model. The techniques are (1) a tornado-diagram approach we employed previously for UCERF2, and (2) an apparently novel probabilistic sensitivity approach that seems better suited to functions of nominal random variables. The new approach produces a reduced-order model with only 60 of the original 57,600 leaves. One can use the results to reduce computational effort in loss analyses by orders of magnitude.

scholarly journals Study of methods for dimension reduction of complex dynamic linear systems models

2018 ◽  
Vol 226 ◽  
pp. 04036
Author(s):  
Yuriy M. Manatskov ◽  
Torsten Bertram ◽  
Danil V. Shaykhutdinov ◽  
Nikolay I. Gorbatenko
Keyword(s):  
Linear Systems ◽  
Main Idea ◽  
Computation Time ◽  
Order Reduction ◽  
Complex Dynamic ◽  
Model Order ◽  
Reduced Order ◽  
Advantages And Disadvantages ◽  
Optimization Stage ◽  
Linear Systems Of Equations

Complex dynamic linear systems of equations are solved by numerical iterative methods, which need much computation and are timeconsuming ones, and the optimization stage requires repeated solution of these equation systems that increases the time on development. To shorten the computation time, various methods can be applied, among them preliminary (estimated) calculation or oversimple models calculation, however, while testing and optimizing the full model is used. Reduced order models are very popular in solving this problem. The main idea of a reduced order model is to find a simplified model that may reflect the required properties of the original model as accurately as possible. There are many methods for the model order reduction, which have their advantages and disadvantages. In this article, a method based on Krylov subspaces and SVD methods is considered. A numerical experiments is given.

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