Parallel RBF and Built-in linear system solvers (in dev branch)

[Wendi-L]

What has been done:

Make RBF sampler work in both serial and parallel modes.

• Facilitate ghost points distribution/collection and ghost point matrix construction.
• Functionalised ghost point related activities.
• Updated C and Fortran wrappers on the new RBF API.

  Removes the Eigen library dependency.

• Established MUI built-in linear algebra namespace, i.e. mui::linalg, with sparse matrix system, two linear system solvers (Gaussian Elimination direct solver and Conjugate Gradient iterative solver), and three preconditioners (Incomplete LU preconditioner, Incomplete Cholesky Preconditioner, Symmetric Successive Over-Relaxation Preconditioner).
• The conjugate gradient solver is based on Algorithm 1 of the following paper: Igor Baratta, Chris Richardson, and Garth Wells. "Performance analysis of matrix-free conjugate gradient kernels using SYCL." International Workshop on OpenCL. 2022.
• The conjugate gradient solver can be worked in both w/o preconditioner mode and with one of the preconditioner modes.
• The "linalg" folder contains three base files (matrix.h, solver.h and preconditioner.h) with implementations in separate files, which makes it easy to maintain and easy to extend in the long run.
• Add unit test code (a separate folder named “test”) to verify arithmetic operations, manipulations and decompositions of the sparse matrix, verify matrix file I/O and verify GE solver and different combinations of preconditioner and CG by comparing calculated results with reference results.
• Add ReadMe.md file for the mui::linalg folder.

  Verifications:

• The RBF sampler is verified by MUI demo 7-pseudo-diffusion. Both conservative mode and consistent mode have been tested.
• The arithmetic operations of the mui::linalg sparse matrix system have been verified by the matrix.cpp code in the “test” folder. More specifically: matrix addition, matrix subtraction, matrix multiplication, matrix transpose, matrix I/O (includes print matrix to the console and matrix file I/O in CSV format), LU decomposition and QR decomposition.
• The mui::linalg Gaussian Elimination solver and Conjugate Gradient solver have been verified with reference results by the solver.cpp code in the “test” folder. The following modes have been verified: TEST_0: CG Solver w/o Preconditioner & w/o Initial matrix Guess; TEST_1: CG solver with ILU Preconditioner & w/o Initial matrix Guess; TEST_2: CG solver with SSOR Preconditioner & w/o Initial matrix Guess; TEST_3: CG solver with IC Preconditioner & with Initial matrix Guess, TEST_4: CG solver with multi-dimensional matrix, TEST_5: GE solver, TEST_6: GE solver with multi-dimensional matrix.

  Future works:

• Generalise ghost cell functions, so that to enable other samplers/algorithms to access and use it.
• Since the RBF sampler is no longer special compared with other samplers, some pieces of code like below can be removed.

If define RBF:
    Do this;
else:
    Do that;

• Since RBF sampler has changed its API, corresponding lines in the Python wrapper have to be changed accordingly (C and Fortran wrappers have been changed already in this PR).