Adaptive Finite Element Mesh Subdivision Method for Integrated Circuits Based on Posteriori Error Estimation

Abstract

The invention provides an integrated circuit self-adaptive finite element mesh subdivision method based on posterior error estimation. The method comprises the following steps: step 1, solving to obtain a finite element numerical solution of a mesh unit; in the super-convergence unit sheet of each grid node, approximately recovering a gradient Gspr with higher-order precision as an accurate valueof the gradient of the solution based on the gradient Gfem of the solution; 2, calculating a relative error and an overall error of each grid cell unit, judging whether an overall error index reachesthe standard or not, If so, ending; 3, iteratively calculating the one-time subdivision frequency of each grid unit; 4, smoothing the subdivision times of the grid units, so that the difference between the subdivision times of the adjacent grid units is not higher than 1; step 5, directly subdividing each grid unit based on the subdivision times of the grid units; step 6, smoothing the subdividedgrid units; 7, turning to the step 1. According to the method, the solution meeting the precision requirement can be obtained through one-time grid cell subdivision and solving, and the solving time of the electromagnetic field problem of the super-large-scale integrated circuit is shortened.

Description

technical field [0001] The invention relates to the technical field of finite element grid subdivision, in particular to an integrated circuit self-adaptive finite element grid subdivision method based on posterior error estimation. Background technique [0002] Electromagnetic field problems can be described by partial differential equations plus boundary conditions, but because the boundary conditions are very complex, it is impossible to obtain an exact solution from the differential equation and its boundary conditions, and an approximate solution can be obtained by numerical calculation methods such as finite elements, and A sufficiently dense mesh is required to obtain a solution to a certain accuracy. Although the speed and storage capacity of computers are constantly improving, for very complex problems, it is not possible to refine the grid infinitely to pursue the accuracy of the solution. specified accuracy requirements. [0003] In order to judge whether the so...

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Problems solved by technology

[0006] In order to overcome at least one defect in the above-mentioned prior art, the present invention provides an integrated circuit adaptive finite element grid subdivision method based on a posteriori error estimation to solve the problem that the traditional adaptive finite element subdivision method requires multiple The problem of subdividing and solving the grid unit to obtain a solution that meets the accuracy requirements is to ensure that once and as few grid units as possible are subdivided and solved to obtain a solution that meets the accuracy requirements. In the case of obtaining a solution that meets the accuracy requirements, Greatly reduces the memory and CPU time required to solve VLSI electromagnetic field problems

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