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Boundary Conditions for Current Density01:25

Boundary Conditions for Current Density

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Extended Versions of Green’s Theorem

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Magnetostatic Boundary Conditions

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Related Experiment Video

Updated: Jun 19, 2026

Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery
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Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery

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Compensated optimal grids for elliptic boundary-value problems.

F Posta1, S Y Shvartsman, C B Muratov

  • 1Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA.

Journal of Computational Physics
|October 6, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient method for solving elliptic problems on unbounded domains, achieving high accuracy at boundaries. The approach enhances computational efficiency and accuracy for 2D and 3D problems, including cell communication models.

Related Experiment Videos

Last Updated: Jun 19, 2026

Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery
06:18

Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery

Published on: December 6, 2024

Area of Science:

  • Computational mathematics
  • Numerical analysis
  • Applied mathematics

Background:

  • Elliptic problems on unbounded domains present significant computational challenges.
  • Accurate solutions are often required only at the domain boundary.
  • Existing methods may lack efficiency or sufficient accuracy for complex problems.

Purpose of the Study:

  • To develop an efficient numerical method for treating elliptic problems on unbounded domains.
  • To achieve high accuracy solutions specifically at the domain boundary.
  • To extend the optimal grid approach for enhanced accuracy and computational efficiency.

Main Methods:

  • Extension of the optimal grid approach using optimal rational approximation of the Neumann-to-Dirichlet map in Fourier space.
  • Modification of the impedance function to compensate for numerical dispersion.
  • Application to nonlinear problems, such as those in cell communication modeling.

Main Results:

  • Achieved spectrally accurate schemes in 2D and fourth-order accurate schemes in 3D problems.
  • Demonstrated no increase in computational complexity with improved accuracy.
  • Successfully applied the method to nonlinear problems in cell communication modeling.

Conclusions:

  • The proposed method offers a significant improvement in efficiency and accuracy for solving elliptic problems on unbounded domains.
  • It provides a robust framework for boundary-focused solutions in both 2D and 3D.
  • The technique is applicable to complex nonlinear problems, broadening its utility in scientific modeling.