ITR/Comp Bio: Computational Tools for Inverse Electromagnetic Problems

schimpf， paul华盛顿州立大学itr /Comp Bio：逆电磁问题的计算工具首席研究员之前开发了一种自适应算法，用于解决复杂三维域中的泊松问题。该算法立即应用于对手术植入除颤器产生的电场进行建模，作为心脏病专家电极放置的指导，该算法将解决时间从3小时缩短到不到10分钟。合乎逻辑的下一步是追求更苛刻的应用，例如那些具有反问题公式的应用。反问题寻求在表面电场测量或建模域外磁场测量的基础上识别体积能量源。一般来说，除非利用了资源的一些先验知识，否则没有唯一的解决方案。逆问题可以在偏微分方程控制域的许多应用中公式化。它们是计算密集型的，因为通常需要许多正向计算来求解逆问题。本工作的主要目的是开发一种基于域的层次空间分解的高效实用的逆算法，并将其与现有的正演算法相结合，推广给需要解决此类问题的研究人员。心脏病学和神经学是两个可以从这些工具的可用性中受益的领域。在临床应用中，这些工具在疾病的诊断和治疗方面可以证明是无价的。在研究应用中，这些工具可以提高我们对系统基本行为的认识。

EIA-0112742Schimpf, PaulWashington State UniversityITR/Comp Bio: Computational Tools for Inverse Electromagnetic ProblemsThe principal investigator previously developed an adaptive algorithm for solving the Poisson problem in complex three-dimensional domains. This algorithm found immediate applicationin modeling the electric field produced by surgically implanted defibrillators as a guide to electrode placement for the cardiologist, where the algorithm reduced solution times from 3 hours to less than 10 minutes.A logical next step is the pursuit of more demanding applications, such as those with an inverse problem formulation. The inverse problem seeks to identify volume energy sources on the basisof electric field measurements on the surface or magnetic field measurements outside of the modeled domain. In general, there is no unique solution unless some a-priori knowledge of thesources is exploited. Inverse problems can be formulated for many applications with domainsgoverned by partial differential equations. They are computationally intensive because many forward computations are typically required for a solution to the inverse problem.The primary aim of this work is to develop an efficient and practical inverse algorithm based on a hierarchical spatial decomposition of the domain, integrate it with the existing forward algorithm, and disseminate it to researchers with a need to solve such problems. Cardiology and neurology are examples of two fields that can benefit from the availability of such tools. In clinical applications, these tools can prove invaluable in the diagnosis and treatment of disease. In research applications, these tools can improve our knowledge of the fundamental behavior of the system.