Parallel Computing Research On The Boundary Element Method For Solving The Forward Problem Of Electrical Impedance Endotomography

Electrical impedance endotomography (EIE) technology is a functional imagingtechnology developed from electrical impedance tomography (EIT). In EIE, the electrodesare placed on the probe of an insulated catheter, and the probe is directly inserted into theinside of interested organs. The excitation currents are injected and the voltages aremeasured using the electrodes, and then the inner impedance distribution of the organs canbe reconstructed. EIE is actually an inverse problem, and solving the forward problem fastand correctly is the basis of the EIE reconstruction. So the research of parallel algorithmsfor EIE forward problem has great significance.In this thesis, boundary element method (BEM) is adopted for solving EIE forwardproblem, and the parallel computing for forward computation is mainly studied. Firstly, theboundary integral equation is derived, and the numerical method is introduced. The EIEforward problem is calculated against two-dimensional concentric circle model andthree-dimensional concentric cylinder model, and the potential distributions on electrodesare achieved. Secondly, the basic theory of parallel computing is studied; the OpenMPprogram model and ScaLAPACK software package are analyzed in details. As to the BEMof solving EIE forward problem, the parallel programs are designed and realized. The loopparallelization is used for forming system matrix and the ScaLAPACK is called for solvinglinear equations. Finally, the parallel experiments are simulated on two-dimensional andthree-dimensional models, parallel computing performances are discussed under variousnumbers of threads, and the acceptable speedup ratio and parallel efficiency are obtained.The results show that apparent accelerations of EIE forward problem are obtained usingparallel computing, which lays a solid foundation for solving inverse problem quickly andaccurately.