Research On The Algorithm For Acceleration Of Numerical Calculation Of Electromagnetic Fields

Silicon-based photonic devices are widely used in optical interconnection systems,optical communication technology and optical computing.Traditional silicon-based photonic devices are designed inefficiently and have great limitations in device size and function.The continuous improvement of the micro-nano photonics production process provides the possibility to make larger precision structures.In recent years,the inverse design of silicon-based micro-nano photonic devices has gradually become a research hotspot,which is essentially designed based on a mathematical optimization calculation.By modeling the target structure and the target performance,optimization calculation and high-performance computing we can get the final device structure.The silicon-based photonic devices obtained by inverse design can theoretically adapt to different sizes and shape structures.However,in the optimization process of inverse design,the degrees of freedom adjustment for spatial structure increase exponentially with the increase of device size and function complexity,and the calculation amount may exceed one trillion billion scales.The numerical calculation time of the electromagnetic fields often doubles with the device size and complexity of the structure.Therefore,research on the algorithm for the acceleration of numerical calculation of electromagnetic fields becomes one of the key problems of the inverse design in silicon-based photonics.The design of silicon-based photonic devices can greatly shorten the research period and reduce the comprehensive cost,which has significant research value.The paper is devoted to the research on the algorithm for the acceleration of numerical calculation of electromagnetic fields,and the main research contents are as follows:1.First,the optimization of algorithm is put forward in combination with the existing calculation of electromagnetic fields in inverse design system.The calculation and background area of silicon-based devices are divided by using preconditioning parameters and Schur complement preconditioning method,and relevant theory of Schur complement preconditioning design are analyzed in detail.The optimized algorithm effectively reduces the scale of calculation matrix.The paper then carries out the performance verification in the 3 x3Hub and 1×2 beam splitter,and the optimized algorithm is 2.95 and 17.9 times the speed of the original inverse design algorithm,demonstrating an improvement in computational speed.Besides,the quantitative relationship between mesh nodes and nonzero in the sparse matrix of Schur complement preconditioning algorithm in 1D,2D and 3D is derived,and its application range is also explained.2.By using the combination of adaptive mesh and Schur complement preconditioning algorithm,the design area and background area of the device are represented by different spatial resolutions.The combined algorithm further reduces the scale of the computation matrix,and the algorithm system based on Schur complement domain decomposition-adaptive mesh achieves a speed that is 17.9 times the original speed in the 1×2 beam splitter,which effectively solves the limited application range of using Schur complement preconditioning method alone,and has a significant speed improvement in the design of larger size 2D devices.3.Combined with the existing inverse design system,this paper designs iterative solvers of CG,COCG,BICG,BICGSTAB,CG and CR,and effectively links the iterative solution algorithms above through linkers to give full play to the advantages of different iterative solvers.In the numerical calculation process of electromagnetic fields,different iterative solution algorithms are selected for different optimization stages,and different iterative solution algorithms are combined through linkers.This method significantly improves the calculation speed in the numerical calculation of electromagnetic fields.Compared with COCG which performs the best when each algorithm works alone,the speed of the BICG-COCG combination is 1.95 times the speed of COCG in the small-scale matrix 1×2 beam splitter,2.19 times in the middle-scale matrix 3×3Hub,and 2.65 times in the large-scale matrix vertical coupler.The results show that the combination of different iterative solution algorithms can be more adapted to the simulation of devices with different sizes and functions,and has strong stability.