quad_mesh

quad_mesh, a MATLAB code which carries out operations involving meshes of quadrilaterals.

The mesh is the collection of quadrilaterals. Each quadrilateral is termed an "element". The points used to define the shape of the quadrilateral (the corners, and sometimes a few more points) are called the "nodes".

Routines are available to:

• evaluate "quality measures" for the mesh;
• create a "node neighbor array" for each node;
• create an "element neighbor array" for each element;
• estimate the integral of a function over the region covered by the mesh;
• plot the nodes and elements of a mesh;
• determine the parts of the mesh that lie on the boundary;
• sample points at random from the region covered by the mesh;
• search a mesh to determine which element contains a point.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

quad_mesh is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

fem2d, a data directory which contains a description and examples of files that describe a 2D finite element model.

fem_io, a MATLAB code which reads or writes node, element and data files defining a finite element model.

fem2d_pack, a MATLAB code which handles various tasks associated with finite element meshes.

mesh_bandwidth, a MATLAB code which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.

mesh_display, a MATLAB code which reads data defining a polygonal mesh and displays it, with optional numbering.

quad_mesh, a data directory which defines a format for storing meshes of quadrilaterals over a 2D region.

quad_mesh_test

quad_mesh_order1_display, a MATLAB code which plots piecewise constant data associated with a mesh of quadrilaterals;

quad_mesh_rcm, a MATLAB code which computes the reverse Cuthill-McKee (RCM) reordering for nodes in a mesh of 4-node quadrilaterals.

triangulation, a MATLAB code which carries out operations involving meshes of triangular elements.

Reference:

1. Hans Rudolf Schwarz,
   Methode der Finiten Elemente,
   Teubner Studienbuecher, 1980,
   ISBN: 3-519-02349-0.
2. Gilbert Strang, George Fix,
   An Analysis of the Finite Element Method,
   Cambridge, 1973,
   ISBN: 096140888X,
   LC: TA335.S77.
3. Olgierd Zienkiewicz,
   The Finite Element Method,
   Sixth Edition,
   Butterworth-Heinemann, 2005,
   ISBN: 0750663200,
   TA640.2.Z54

Source Code:

• adj_bandwidth.m, omputes the bandwidth of an adjacency matrix.
• adj_perm_bandwidth.m, omputes the bandwidth of a permuted adjacency matrix.
• adj_set_q4_mesh.m, sets the adjacencies in a Q4 mesh.
• adj_size_q4_mesh.m, counts adjacencies in a Q4 mesh.
• area_q4_mesh.m, computes areas of elements in a Q4 mesh;
• area_quad.m, return the area of a quadrilateral;
• boundary_edge_count_q4_mesh.m, counts boundary edges.
• boundary_edge_count_euler_q4_mesh.m, counts boundary edges using Euler's formula.
• example1_q4_mesh.m, sets up example #1 Q4 mesh.
• example1_q4_mesh_size.m, sets sizes for example #1 Q4 mesh.
• example1_q4_mesh_plot.m, plots example #1 Q4 mesh.
• example2_q4_mesh.m, sets up example #2 Q4 mesh.
• example2_q4_mesh_size.m, sets sizes for example #2 Q4 mesh.
• example2_q4_mesh_plot.m, plots example #2 Q4 mesh.
• example3_q4_mesh.m, sets up example #3 Q4 mesh.
• example3_q4_mesh_size.m, sets sizes for example #3 Q4 mesh.
• example3_q4_mesh_plot.m, plots example #3 Q4 mesh.
• example4_q4_mesh.m, sets up example #4 Q4 mesh.
• example4_q4_mesh_size.m, sets sizes for example #4 Q4 mesh.
• example4_q4_mesh_plot.m, plots example #4 Q4 mesh.
• fem_bandwidth.m, determines the bandwidth associated with the finite element mesh;
• file_column_count.m, counts the number of columns in the first line of a file.
• file_row_count.m, counts the number of row records in a file.
• i4_modp.m, computes the positive modulus of an I4.
• i4_wrap.m, wraps an I4.
• i4col_compare.m, compares two columns of an I4COL;
• i4col_sort_a.m, ascending sorts the columns of an I4COL;
• i4col_sorted_unique_count.m, counts the number of unique elements in a sorted I4COL;
• i4col_swap.m, swaps two columns of an I4COL;
• i4mat_data_read.m, reads data from an I4MAT file..
• i4mat_header_read.m, reads the header from an I4MAT file.
• i4mat_transpose_print.m, prints the transpose of an I4MAT.
• i4mat_transpose_print_some.m, prints some of the transpose of an I4MAT.
• i4mat_write.m, writes an I4MAT file.
• i4vec_print.m, prints an I4VEC.
• mesh_base_one.m detects and corrects 0-based indexing.
• node_order_q4_mesh.m, determines the order of nodes in a Q4 mesh.
• neighbor_elements_q4_mesh.m, determines element neighbors in a Q4 mesh.
• plot_q4_mesh.m, plots a Q4 mesh.
• r8_uniform_01.m, returns a unit pseudorandom R8.
• r8mat_data_read.m, reads a table from an R8MAT file.
• r8mat_header_read.m, reads a table header from an R8MAT file.
• r8mat_transpose_print.m, prints the transpose of an R8MAT;
• r8mat_transpose_print_some.m, prints some of the transpose of an R8MAT;
• r8mat_write.m, writes an R8MAT file.
• r8vec_print.m, prints an R8VEC.
• r8vec_uniform_01.m, returns a unit pseudorandom R8VEC.
• reference_to_physical_q4.m maps points in a Q4 reference triangle into physical space.
• s_len_trim.m, returns the length of a character string to the last nonblank.
• s_word_count.m, counts the number of words in a string.
• sample_q4_mesh.m, randomly samples a point from a Q4 mesh;
• sample_quad.m, randomly samples a point from a quadrilateral;
• sort_heap_external.m, externally sorts a list of values into ascending order;
• triangle_area.m, returns the area of a triangle;
• triangle_sample.m, randomly samples a point from a triangle;