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Lecture 31a, sparse solution of PDE 


When the number of degrees of freedom gets large, the size of
the matrix for the system of simultaneous equations may get
larger than acceptable for your computer.

For example a four dimensional PDE with 10 DOF in each dimension
has 10^4 = 10,000 DOF. The non sparse simultaneous equations
would require at least 10,000 by 10,000 entries, 10^8 times
8 bytes = 0.8GB.

Much larger PDE's, need to be solved.

A sparse matrix stores only the non zero entries.
A system of simultaneous equations does not have a unique
solution if any row is all zeros, thus a sparse structure
has at least one entry of each row. Then in each row,
the column index and value are stored for the non zero
values. Typical spare data structures use a singly linked
list for each row, keeping the column index in increasing
numerical order.

Optimized code is typically written for inserting and
adding entries, solving simultaneous equations, vector
times matrix multiplication and a few other operations.

For various languages, the sparse packages are shown with
the initial test programs and several PDE solutions.


"C" implementation of sparse

"C" source code sparse.c
"C" header file sparse.c
"C" test code test_sparse.c
test output test_sparse_c.out
"C" more test code test1_sparse.c
test output test1_sparse_c.out
simple conversion to sparse_abc.c
output of sparse_abc_c.out
"C" source code pde44_sparse.c
test_output pde44_sparse_c.out



Ada implementation of sparse

For subscripts starting with zero
Ada source code sparse.adb
Ada package specification sparse.ads
Ada test code test_sparse.adb
test output test_sparse_ada.out
For subscripts starting with one
Ada source code sparse1.adb
Ada package specification sparse1.ads
Ada test code test_sparse1.adb
test output test_sparse1_ada.out
simple conversion to sparse_abc.adb
output of sparse_abc_ada.out
Ada source code pde44_sparse.adb
test_output pde44_sparse_ada.out



Java implementation of sparse

Java source code sparse.java
Java test code test_sparse.java
test output test_sparse_java.out
simple conversion to sparse_abc.java
output of sparse_abc_java.out
Java source code pde44_sparse.java
test_output pde44_sparse_java.out



Fortran implementation of sparse

For subscripts starting with zero
Fortran source code sparse.f90
Fortran test code test_sparse.f90
test output test_sparse_f90.out
For subscripts starting with one
Fortran source code sparse1.f90
Fortran test code test_sparse1.f90
test output test_sparse1_f90.out
Fortran source code pde44_sparse.f90
test_output pde44_sparse_f90.out




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