FEA

AbstractFEASolver

Abstract type for all FEA solvers in TopOpt. GenericFEASolver is the concrete implementation.

AbstractPhysics

Abstract type for the physics model dispatched on by GenericFEASolver. Subtypes: LinearElasticity (structural mechanics, dim DOFs/node) and HeatTransfer (heat conduction, 1 DOF/node).

LinearElasticity

Physics tag for structural-mechanics problems. Selects linear-elasticity element matrices and assembly (dim DOFs per node).

HeatTransfer

Physics tag for heat-conduction problems. Selects heat-transfer element matrices and assembly (1 DOF per node).

AbstractLinearSolver

Abstract type for the linear-system algorithm used inside GenericFEASolver. Subtypes: DirectSolver (factorization), CGAssemblySolver (CG with an assembled sparse matrix), CGMatrixFreeSolver (matrix-free CG).

SolverResult

Abstract type for the result returned by an FEA solver.

DirectSolver

Direct linear solver using Cholesky (or QR) factorization. The most robust option for small to medium problems.

CGAssemblySolver

Conjugate-gradient solver with an assembled sparse matrix. Suitable for larger problems where a factorization is too expensive in memory.

CGMatrixFreeSolver

Matrix-free conjugate-gradient solver. Avoids assembling the global stiffness matrix entirely, applying element matrices on the fly. Does not yet support inhomogeneous Dirichlet BCs.

GenericFEASolver

Unified FEA solver with orthogonal physics and linear-solver dispatch. Use the FEASolver factory constructor instead of constructing this directly.

FEASolver(Physics, Solver, problem; kwargs...) -> GenericFEASolver
FEASolver(Solver, problem; kwargs...) -> GenericFEASolver

Factory constructor for the unified FEA solver. The second form infers the physics type from the problem type. Keyword arguments: quad_order, xmin, penalty, prev_penalty, qr, cg_max_iter, abstol, preconditioner, conv.

MatrixFreeOperator

Linear operator that applies the global stiffness matrix without assembling it, by looping over element matrices. Used by CGMatrixFreeSolver.

MatrixOperator

Linear operator wrapping an assembled matrix for use with IterativeSolvers' cg!.

ConvergenceCriteria

Abstract type for CG convergence criteria. Subtypes: DefaultCriteria, EnergyCriteria.

DefaultCriteria

Default CG convergence criterion based on the residual norm.

EnergyCriteria

Energy-based CG convergence criterion, checking the relative energy norm. Useful for stiff systems where the residual norm is a poor indicator.

simulate(solver, x)

Run a forward FEA solve for the design x and return the displacement/temperature field. Convenience wrapper around the solver call operator.

cg_solve!(solver, op, rhs, lhs, precond_matrix; initially_zero=true)

Solve the linear system with the solver's preconditioned conjugate-gradient settings, writing the solution into lhs.