Rodin/Solver/CHOLMOD.h file

CHOLMOD supernodal Cholesky factorization solver wrapper.

This header provides a wrapper for CHOLMOD from SuiteSparse, a high-performance solver for sparse symmetric positive definite systems using supernodal LLT Cholesky factorization.

Algorithm

CHOLMOD computes:

\[ A = LL^T \]

where $ L $ is lower triangular. The supernodal method groups columns with similar sparsity patterns to exploit dense matrix operations (BLAS) for improved performance.

Applicability

  • Symmetric positive definite sparse matrices
  • Large-scale finite element problems
  • Structural mechanics
  • Heat transfer problems
  • Graph Laplacian systems

Usage Example

Problem problem(u, v);
problem = Integral(Grad(u), Grad(v)) - Integral(f, v);

Solver::CHOLMOD::SupernodalLLT solver(problem);
solver.solve();