Module functions 

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Functions

add3

Element-wise addition of two 3D vectors.

allen_cahn_step

Advance the Allen-Cahn phase-field φ by one explicit time step.

arlequin_blend_energy

Handshake zone energy correction to remove double-counting in concurrent multiscale coupling.

atomistic_temperature

Compute the instantaneous temperature of a group of atoms via the equipartition theorem: T = 2 KE / (3 N k_B).

cauchy_born_modulus

Linear elasticity tangent modulus from a set of atom-pair bond stiffnesses.

cauchy_born_stress_1d

Cauchy-Born rule: compute the first Piola-Kirchhoff stress from a deformation gradient F using a linearised atomistic model.

cell_problem_1d

Solve the scalar periodic cell problem via finite differences to obtain the effective conductivity in the x-direction.

centre_of_mass_velocity

Compute the centre-of-mass velocity of a group of atoms.

cg_bond_force

Compute harmonic bond force between two CG beads.

check_scale_separation

Check scale separation: verifies that the micro length scale is at least factor times smaller than the macro length scale.

dot3

Dot product of two 3D vectors.

hill_mandel_error

Compute the Hill-Mandel macrohomogeneity condition error.

hmm_estimate_flux

Compress micro-scale simulation data into a macro-scale flux estimate.

homogenize_two_phase

Compute homogenized (effective) properties of a two-phase unit cell.

lennard_jones_force

Lennard-Jones force magnitude (scalar, positive = repulsive).

lennard_jones_potential

Lennard-Jones pair potential energy between two atoms.

mat3_add

Add two 3×3 matrices stored row-major.

mat3_frob

Frobenius norm of a 3×3 matrix.

mat3_identity

Identity 3×3 matrix.

mat3_scale

Scale a 3×3 matrix.

mat3_vec

Multiply a 3×3 row-major matrix by a 3-vector.

mean_squared_displacement

Compute the mean squared displacement (MSD) of atoms relative to their reference positions.

multigrid_vcycle

Multigrid V-cycle for a 1-D Poisson problem.

neb_step

Perform one NEB step with spring forces.

norm3

Euclidean norm of a 3D vector.

normalize3

Normalize a 3D vector to unit length.

prolongation_linear

Prolongation operator: interpolate a coarse-grid vector to the fine grid using piecewise-linear interpolation.

restriction_l2

Restriction operator: project a fine-grid vector onto a coarse grid by L2-projection (average over blocks).

scale3

Scale a 3D vector by a scalar.

solve_macro_diffusion_1d

Solve 1-D steady-state diffusion with heterogeneous effective conductivity using a finite-difference discretisation.

sub3

Element-wise subtraction of two 3D vectors.

umbrella_free_energy

Compute the coarse-grained potential energy surface along a reaction coordinate.

virial_stress_tensor

Hardy stress tensor estimator for the atomistic region.