Method for quickly constructing low-dimensional reduced-basis space in electromagnetic scattering modeling

Abstract

The invention discloses a method for quickly constructing a low-dimensional reduced-basis space in electromagnetic scattering modeling. The method comprises the steps of firstly, selecting out a domain or a boundary which determines a final output variable from geometric domains or geometric boundaries of a to-be-simulated structure, wherein the selected domain or boundary is called as a main domain or a main boundary; secondly, based on an original high-dimensional model, constructing a high-dimensional partial model about a variable in the main domain or on the main boundary, and constructing a reduced-basis space for the high-dimensional partial model in a parameterization environment, wherein the obtained reduced-basis space is called as a partial reduced-basis space; and finally, projecting the high-dimensional partial model to the partial reduced-basis space to obtain an approximate low-dimensional model, and replacing solving of the original high-dimensional model with solving of the low-dimensional model, thereby improving the solving efficiency of a simulation model is improved. The method is especially suitable for the situation that the final output variable is determined only by a partial solution in the high-dimensional model. Compared with a conventional reduced-basis method, the method has the advantages that the dimensions of the reduced-basis space are further reduced (correspondingly, the dimensions of the low-dimensional model are further reduced) and the construction speed of the reduced-basis space is greatly increased.

Description

technical field [0001] The invention belongs to the field of electromagnetic field scattering measurement, and more specifically relates to a method for quickly constructing a low-dimensional base-reduction space. Background technique [0002] In the field of electromagnetic field scattering measurement, the process of extracting the required parameters according to the measurement signal involves multiple forward modeling, that is, it is necessary to select many values ​​for the required parameters and solve the corresponding simulation model. The simulation model is generally solved by traditional numerical methods, such as finite element method, finite time domain difference method, boundary element method, etc. In the actual operation process, the above numerical method transforms the model to be simulated into a high-dimensional linear equation for solution, that is, transforms it into the solution of a high-dimensional model. Although there are many fast solution meth...

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Problems solved by technology

Therefore, it is uneconomical to reduce the order of the high-dimensional system by using the basis reduction method, which not only makes the construction of the basis reduction space extremely time-consuming, but also the final low-dimensional model still contains redundant information, which affects its Solution efficiency

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