scholarly journals Schur Complement Preconditioners for Surface Integral-Equation Formulations of Dielectric Problems Solved with the Multilevel Fast Multipole Algorithm

2011 ◽  
Vol 33 (5) ◽  
pp. 2440-2467 ◽  
Author(s):  
Tahİr Malas ◽  
Levent Gürel
Keyword(s):  
Integral Equation ◽  
Schur Complement ◽  
Fast Multipole ◽  
Surface Integral ◽  
Surface Integral Equation ◽  
Multilevel Fast Multipole Algorithm ◽  
Fast Multipole Algorithm

scholarly journals The Application of Improved Spherical Harmonics Expansion-Based Multilevel Fast Multipole Algorithm in the Solution of Volume-Surface Integral Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Jinbo Liu ◽  
Mang He ◽  
Zengrui Li ◽  
Jianxun Su
Keyword(s):  
Integral Equation ◽  
Spherical Harmonics ◽  
Hardware Acceleration ◽  
Memory Requirement ◽  
Fast Multipole ◽  
Surface Integral ◽  
Surface Integral Equation ◽  
Multilevel Fast Multipole Algorithm ◽  
Spherical Harmonics Expansion ◽  
Fast Multipole Algorithm

During the solution of volume-surface integral equation (VSIE), to reduce the core memory requirement of the radiation patterns (RPs) of the basis functions, an improved spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA) using the mixed-potential representation and the triangle-/tetrahedron-based grouping scheme is applied. Numerical results show that accompanying with a faster speed, the memory requirement of the RPs in the improved SE-MLFMA is several times less than that in the conventional MLFMA without compromising accuracy. A result employing the OpenMP parallelization and vector arithmetic logic unit (VALU) hardware acceleration technique is also shown to illustrate the robustness and scalability of the improved SE-MLFMA method.

scholarly journals Combination of MLFMA and ACA to Accelerate Computation of Scattering from Underground Targets

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Zhiwei Liu ◽  
Dan Tang ◽  
Zhanyang Zhang ◽  
Yueyuan Zhang ◽  
Xiaoli Wang ◽  
...  
Keyword(s):  
Integral Equation ◽  
Nondestructive Evaluation ◽  
Method Of Moments ◽  
Impedance Matrix ◽  
Computation Complexity ◽  
Surface Integral ◽  
Efficient Simulation ◽  
Urban Construction ◽  
Multilevel Fast Multipole Algorithm ◽  
Fast Multipole Algorithm

Electromagnetic nondestructive evaluation of underground targets is of great significance for the safety of urban construction. Based on the accurate and efficient simulation of scattering, we can detect the underground targets successfully. As one of the most popular numerical methods in electromagnetics, surface integral equations solved by method of moments (MoM) are used to simulate the scattering from underground targets in this paper. The integral equation is discretized by RWG basis and Galerkin testing. Multilevel fast multipole algorithm (MLFMA) is used to decrease the computation complexity and memory cost. However, the octree used in MLFMA is not applied for rough surfaces and targets together; both the surface and target need to construct octree separately. Since the combination of MLFMA and ACA can build a more efficient method to compute scattering from underground targets, adaptive cross approximation (ACA) is used to compress the impedance matrix instead of MLFMA for the coupling action between the rough surface and target. That is to say that, when calculating the scattering of two targets, target self-interaction is suitable for MLFMA calculation and the coupling between targets is approximated by ACA. Numerical results demonstrate the accuracy and efficiency of our proposed method.

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