MassBinding

Published configurations

Measures the MassBinding workload through its public library pipeline.

Measured operation

Measures scalar-weighted H1 mass preparation and component contraction.

Mathematical foundation

For scalar weight \(\rho\), the discrete component entries satisfy \[ A_{bm+e,am+c}=\delta_{ec}S_{ba},\qquad S_{ba}=\sum_q w_q D_q\rho(x_q)\phi_a(x_q)\overline{\phi_b(x_q)}. \] Matrix fields use their local row-major component convention and the Frobenius product. Unit mass uses \(\rho=1\). Weighted cases use \(\rho=s(2+x_0)\) for real fields and \(\rho=s(2+x_0+i/2)\) for complex fields. This is not a Hermitian symmetry claim when the coefficient is complex.

Measurement boundary

One-cell public binding includes mapped quadrature, scalar reference-data lookup and complete local matrix preparation. Construction, independent qualification and final repeated-entry checks are untimed. Scatter, load assembly and projection solves belong to their owning consumer modules.

The original expression-entry loop qualifies only the scalar block. Every component entry is then checked exactly against the retained first block, including structural zeros. A perturbed scalar block must be rejected. The reference storage is therefore scalar-sized, not a second full component matrix. Doubling the borrowed coefficient scale after timing checks replacement rather than accumulation of stale operator values. Explicit orders define discrete operators; underintegrated samples are not claims about polynomial integration exactness or PDE convergence.

Scalar weights are measured in both operand orders. Although \(\rho u=u\rho\) algebraically, their expression types and local quadrature dispatch may differ. The dispatch counter records this implementation property without requiring one particular implementation. General matrix coefficients are not commuted.

Recorded results

Each case retains its original inputs, iteration policy and correctness checks. Raw reports preserve counters, repetitions and the Google Benchmark context. CPU, wall and manually supplied times are labeled separately; unlike operations and configurations are not averaged together.

Timing history

RodinH1MassBindingBenchmarks · auto · regular · ranks: 1