FEA Cost Estimator

Pick your mesh size and matrix bandwidth; compare how six classical linear solvers would scale. Ops are order-of-magnitude flop counts. Time assumes a sustained flop rate you set below.

Degrees of freedom (N)10,000

Effective bandwidth / nnz per row100

Sustained flop rate (GFLOPS)50 GFLOPS

SolverCategoryOpsTimeELC note

LU (direct, dense)O(N³) factorization + O(N²) solvedirect333.43G6.7 sinterior per step, but closed-form for n≥5 is boundary via Abel-Ruffini

Cholesky (SPD, dense)O(N³/6) factorization + O(N²) solvedirect166.77G3.3 sinterior per step, halves LU memory when applicable

Banded LU (bandwidth bw)O(N · bw²) factorization + O(N · bw) solvedirect101.00M2.0 msinterior, huge win for 1D / structured meshes

Conjugate Gradient (iterative)~50 iters × (5 · N · nnz) per iterationiterative250.00M5.0 msstrictly ELC-interior per iteration; converges in O(√κ · log(1/ε)) steps

GMRES (non-SPD, iterative)~80 iters × (6 · N · nnz) + O(k² · N) orthoiterative489.00M9.8 msinterior per step; restart size k adds O(k²N) orthogonalization

Algebraic multigridcheapest~15 V-cycles × 12N ops eachiterative1.80M36 µsinterior; the cheapest scalable solver for elliptic problems