Helpers

Weakform Helpers

WeakForm/Expr helpers (symbolic operators).

fluxfem.helpers_wf.I(dim: int) → Expr

Identity matrix of size dim.

fluxfem.helpers_wf.action(v, s) → Expr

Test-function action: v.val * s -> (q, n_ldofs).

fluxfem.helpers_wf.dOmega() → Expr

Volume quadrature measure (w * detJ).

fluxfem.helpers_wf.ddot(a, b, c=None) → Expr

Double contraction or a^T b c.

fluxfem.helpers_wf.det(a) → Expr

Determinant of a square matrix.

fluxfem.helpers_wf.dot(a, b) → Expr

Dot product or vector load helper.

fluxfem.helpers_wf.ds() → Expr

Surface quadrature measure (w * detJ).

fluxfem.helpers_wf.gaction(v, q) → Expr

Gradient action: v.grad · q -> (q, n_ldofs).

fluxfem.helpers_wf.grad(field) → Expr

Return basis gradients for a scalar or vector FormField.

fluxfem.helpers_wf.inner(a, b) → Expr

Inner product over the last axis (tensor-level).

fluxfem.helpers_wf.inv(a) → Expr

Matrix inverse.

fluxfem.helpers_wf.linear_stress(sym_grad_u, p)

Linear elastic stress from symmetric gradient in Voigt notation.

fluxfem.helpers_wf.log(a) → Expr

Natural logarithm.

fluxfem.helpers_wf.matmul(a, b) → Expr

FEM-specific batched contraction (same semantics as @).

fluxfem.helpers_wf.matmul_std(a, b) → Expr

Standard matrix product (jnp.matmul semantics).

fluxfem.helpers_wf.normal() → Expr

Surface normal vector (from SurfaceFormContext).

fluxfem.helpers_wf.outer(a, b) → Expr

Outer product of scalar fields: outer(v, u) (test, trial).

fluxfem.helpers_wf.sdot(a, b) → Expr

Surface dot product or vector load helper.

fluxfem.helpers_wf.sym_grad(field) → Expr

Return symmetric-gradient B-matrix for a vector FormField.

fluxfem.helpers_wf.traction(field, n, p)

Traction vector for a field using linear elastic stress.

fluxfem.helpers_wf.transpose(a) → Expr

Swap the last two axes.

fluxfem.helpers_wf.transpose_last2(a) → Expr

Swap the last two axes.

fluxfem.helpers_wf.voigt_to_tensor(sym_grad_u, p=None)

Convert Voigt-form symmetric gradient to a 3x3 tensor.

Uses the standard Voigt mapping with 1/2 on shear terms.

Tensor-Style Helpers

Tensor helpers (array operators).

fluxfem.helpers_ts.ddot(a: ArrayLike, b: ArrayLike, c: ArrayLike | None = None) → ArrayLike

Double contraction on the last two axes.

• ddot(a, b): sum_ij a_ij * b_ij

• ddot(a, b, c): a^T b c (Voigt-style linear elasticity blocks)

fluxfem.helpers_ts.dot(a: FormFieldLike | ArrayLike, b: ArrayLike) → ArrayLike

Batched matrix product on the last two axes.

If the first argument is a FormField, dispatch to vector_load_form to build the linear form contribution for a vector load.

fluxfem.helpers_ts.sym_grad(field: FormFieldLike) → jax.numpy.ndarray

Symmetric gradient operator for vector mechanics (small strain).

Parameters:

field (FormField-like) –

Must provide:

• field.gradN : (n_q, n_nodes, 3)

• field.basis.dofs_per_node (usually 3)

Returns:

B – (n_q, 6, dofs_per_node*n_nodes) Voigt order [xx, yy, zz, xy, yz, zx] Such that eps_voigt(q,:) = B(q,:,:) @ u_elem

Return type:

jnp.ndarray

fluxfem.helpers_ts.transpose_last2(a: jax.numpy.ndarray) → jax.numpy.ndarray

Swap the last two axes (batched transpose).