论文标题
脑电图中对称配方的新的无细化预处理
A New Refinement-Free Preconditioner for the Symmetric Formulation in Electroencephalography
论文作者
论文摘要
对称配方广泛用于脑电图正向问题的准确解决方案，这会引起第一种，条件不足的操作员，不适合用于复杂的建模场景。这项工作基于对所涉及的运算符的准确频谱分析提出了一种新颖的预处理策略，该策略与其他基于Calderón的方法不同，不需要对原始网格的barycentric进行完善（即，不需要双矩阵）。新公式的离散化产生了良好的条件，对称，正定系统矩阵，可以通过快速迭代技术有效地求解。规范和逼真的头模型的数值结果验证了所提出的配方的有效性。
Widely employed for the accurate solution of the electroencephalography forward problem, the symmetric formulation gives rise to a first kind, ill-conditioned operator ill-suited for complex modelling scenarios. This work presents a novel preconditioning strategy based on an accurate spectral analysis of the operators involved which, differently from other Calderón-based approaches, does not necessitate the barycentric refinement of the primal mesh (i.e., no dual matrix is required). The discretization of the new formulation gives rise to a well-conditioned, symmetric, positive-definite system matrix, which can be efficiently solved via fast iterative techniques. Numerical results for both canonical and realistic head models validate the effectiveness of the proposed formulation.
