Li, JunpuChen, WenQin, QinghuaFu, Zhuojia2023-12-110898-1221http://hdl.handle.net/1885/309747A modified multilevel algorithm for solving the excessive storage requirements and ill-conditioning encountered in the boundary-type discretization method is proposed. The modified multilevel algorithm is an extension of the modified dual-level algorithm from dual levels to multiple levels. The method is a kernel-independent method. The core idea is the layer-by-layer calculation and then layer-by-layer correction. Making use of a multilevel structure, the original sparse matrix of the modified dual-level algorithm breaks down into a series of smaller sparse matrices corresponding to different fine meshes. The final matrix to be solved is hereby transformed to a series of smaller sparse matrices instead of a fully-populated matrix. The preconditioning effect originating from the recursive computations among the coarse mesh and fine meshes constitutes its core competitive attribute. The method evaluates far-field contributions only by the coarse mesh and uses a gradual approach to evaluate the near-field contributions. The storage requirements and computing complexity are hereby further reduced significantly.The work was supported by the Fundamental Research Funds for the Central Universities (Grant Nos. 2018B40714, 2017B709X14), the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX17_0488), the National Science Funds of China (Grant Nos. 11572111, 11772119), and the Postgraduate Scholarship Program from the China Scholarship Council (Grant No. 201706710107).application/pdfen-AU© 2018 Elsevier Ltd.Modified multileve lalgorithmModifieddual-level algorithmBoundary-type discretization methodsLaplace equationHelmholtz equation201910.1016/j.camwa.2018.12.0122022-09-04