The computational performance of a high-order coupled FEM/BEM procedure in electropotential problems

Area of Science:

• Computational Electrophysiology
• Numerical Methods in Electromagnetics

Background:

• Electropotential problems are common in bioengineering and physics.
• Traditional boundary element methods (BEM) and finite element methods (FEM) have limitations in accuracy and computational cost.
• A C1 continuous method (value and derivative continuous) is needed for improved performance.

Purpose of the Study:

• To analyze the computational performance of a coupled cubic Hermite boundary element/finite element (BEM/FEM) procedure.
• To quantify the behavior of this high-order method for electropotential problems.
• To compare the new method against traditional BEM/FEM and other published computational techniques.

Main Methods:

• Development and application of a coupled cubic Hermite BEM/FEM procedure.
• Solving dipole in spheres problems with varying parameters (dipole orientation, location, conductivity).
• Comparison of results with traditional linear/constant element BEM and other published methods.

Main Results:

• The cubic Hermite BEM/FEM procedure demonstrated significantly better accuracy and convergence.
• A notable reduction in computational time (CPU time) was observed compared to traditional methods.
• The high-order method achieved improved solution accuracy with fewer solution degrees of freedom.

Conclusions:

• The coupled cubic Hermite BEM/FEM procedure is a highly efficient and accurate method for electropotential problems.
• This high-order approach offers significant advantages over traditional numerical methods.
• The method shows promise for complex bioelectrical modeling applications.