Vectorized 3D mesh refinement and Primal Hybrid FEM

This MATLAB package is developed by N. Harish, G. Sharat , J. Valdman and S. K. Acharya (Date: 01/08/2025).

It is supplement to the paper "Vectorized 3D mesh refinement and implementation

of primal hybrid FEM in MATLAB". The reader should consult that paper for more information.

1. General information on the package

There are two directories when the package is unzipped:

3DPHFEM Elliptic problem with mixed boundary condition

3DUniformRedRefinement

[1]. "Vectorized 3D mesh refinement and implementation of primal hybrid FEM

in MATLAB", N. Harish, G. Sharath, J. Valdman and S. K. Acharya.

The paper [1] presents the overall theory, describes the software package and the examples in detail.

2. Installation Instructions:

i. Unzip Files:

- Download and unzip all the files associated with the package.

ii. Open MATLAB:

- Launch MATLAB on your system.

iii. Set Path:

- Set the proper path to the directory containing the MATLAB modules.

- This ensures that MATLAB can access the required files.

iv. Run the Package:

- With the path properly set, the package is now ready to run.

3. Open the directories

i. 3DPHFEM Elliptic problem with mixed boundary condition Directory:

- Contains MATLAB modules for computing the numerical approximation of a second-order elliptic problem.

- Run "Main.m", which loads initial mesh data from <InitialMesh.m>.

- Volume force and boundary data are provided as M-files: <f.m>, <u_d.m>.

- "StiffMassPH.m" computes stiffness and mass matrices along with the load vector.

- "Multiplier.m" computes the matrix C (Lagrangian multiplier matrix).

- Uses a reduced linear system of equations and Schur Complement method in "Main.m" to calculate a discrete solution

ii. 3DUniformRedRefinement Directory

-Contains MATLAB modules for computing the 3D uniform red refinements.