A Comparison between the hp-version of Finite Element Method with EIDORS for Electrical Impedance Tomography

Area of Science:

• Computational Mathematics
• Biomedical Engineering
• Electrical Engineering

Background:

• Electrical Impedance Tomography (EIT) image reconstruction typically uses the conventional Finite Element Method (h-FEM).
• h-FEM requires a large number of nodes and elements for accurate simulations, leading to high computational costs.
• The high-order Finite Element Method (p-FEM) increases polynomial order but keeps mesh size constant.

Purpose of the Study:

• To investigate the application of the hp-version of Finite Element Method (hp-FEM) for forward modeling in EIT image reconstruction.
• To compare the performance of hp-FEM against the conventional h-FEM in terms of accuracy and computational efficiency.
• To demonstrate the advantages of combining decreased element size (h) and increased polynomial order (p) in EIT.

Main Methods:

• Implementation of the hp-FEM for EIT forward modeling.
• Comparison of hp-FEM with h-FEM using Signal-to-Noise Ratio (SNR) as a performance metric.
• Numerical simulations to evaluate image reconstruction accuracy and computational resource requirements.

Main Results:

• The hp-FEM achieved a significantly higher SNR (42db) compared to h-FEM (9db).
• hp-FEM requires fewer nodes, resulting in reduced computational time and memory usage.
• Numerical results confirmed that hp-FEM provides better performance in EIT image reconstruction than h-FEM.

Conclusions:

• The hp-FEM is a more accurate and computationally efficient method for EIT forward modeling and image reconstruction.
• Combining mesh refinement (h) and increased polynomial order (p) offers substantial benefits over traditional h-FEM.
• This study validates the superior performance of hp-FEM for advancing EIT applications.