Custom edge‐element FEM solver and its application to eddy‐current simulation of realistic 2M‐element human brain phantom

Abstract

Extensive research papers of three-dimensional computational techniques are widely used for the investigation of human brain pathophysiology. Eddy current analyzing could provide an indication of conductivity change within a biological body. A significant obstacle to current trend analyses is the development of a numerically stable and efficiency-finite element scheme that performs well at low frequency and does not require a large number of degrees of freedom. Here, a custom finite element method (FEM) solver based on edge elements is proposed using the weakly coupled theory, which separates the solution into two steps. First, the background field (the magnetic vector potential on each edge) is calculated and stored. Then, the electric scalar potential on each node is obtained by FEM based on Galerkin formulations. Consequently, the electric field and eddy current distribution in the object can be obtained. This solver is more efficient than typical commercial solvers since it reduces the vector eddy current equation to a scalar one, and reduces the meshing domain to just the eddy current region. It can therefore tackle complex eddy current calculations for models with much larger numbers of elements, such as those encountered in eddy current computation in biological tissues. An example is presented with a realistic human brain mesh of 2 million elements. In addition, with this solver, the equivalent magnetic field induced from the excitation coil is applied, and therefore there is no need to mesh the excitation coil. In combination, these significantly increase the efficiency of the solver. Bioelectromagnetics. 39:604-616, 2018.

PSO/DE combined with simulation current method for the magnetic field under transmission lines in 3D calculation model

“…MAXWELL software was used to simulate and solve the same model. For this practical problem, the simulation conditions are as follows 39,40 : Maxwell 3D Version 6 is the analysis type; The boundary condition is the default natural boundary condition in software. The excitation condition is current; solution type is magnetostatic; Mesh type and size are adaptive.…”

Analysis of Tilt Effect on Notch Depth Profiling Using Thin-Skin Regime of Driver-Pickup Eddy-Current Sensor

“…By putting mesh information of all discretised subdomains together, the problem becomes finding a solution of equations with a sparse stiffness matrix. Techniques have been proposed for hastening the solving process using FE A-V form Galerkin methods, including polishing the sparse stiffness matrix, re-ordering and incomplete LU decomposing, optimised initial preconditioner, perturbed matrix, and weakly coupled effect [8,19,[23][24][25]. In addition, other FE models, including the use of reduced magnetic vector potential [26] and alternating current field measurement (ACFM) [27], have been utilised to calculate the field and sensor response.…”

Analysis of Tilt Effect on Notch Depth Profiling Using Thin-Skin Regime of Driver-Pickup Eddy-Current Sensor

“…By putting mesh information of all discretised subdomains together, the problem becomes finding the solution of equations with sparse stiffness matrix. Techniques have been proposed for hastening the solving process using FE A-V form Galerkin methods, including polishing the sparse stiffness matrix -the re-ordering and incomplete LU decomposing, optimised initial preconditioner, perturbed matrix, and weakly coupled effect [8,19,[23][24][25]. Besides, other FE models including the use of reduced magnetic vector potential [26] and alternating current field measurement (ACFM) [27] have been utilised to calculate the field and sensor response.…”