NamedMassKernel

Published configurations

Named mass-kernel lifecycle and within-assembly reference reuse.

Measured operation

Measures the production named mass kernel without global assembly.

Mathematical foundation

For the component basis \(\Phi_{a,c}=\phi_a E_c\), the local matrix is \(A_{bm+e,am+c}=\delta_{ec}S_{ba}\). The scalar block is evaluated independently by the original expression-entry quadrature loop. Weighted scopes use \(\rho=s\alpha\), with \(\alpha=2\) over the reals and \(\alpha=2+i/2\) over the complex numbers. The borrowed scale is one during timing and two during the final coefficient-replacement check. Unweighted scopes use \(\rho=1\). A complex coefficient does not imply Hermitian symmetry. The requested order is the production basis-order sum; comparison certifies that discrete operator, not rational-pyramid exactness.

Architecture and measurement boundary

FreshKernel includes construction, coefficient cloning where applicable, reference-cache creation, computation and kernel destruction. Output storage is retained. CachedKernel retains the same kernel and its prepared reference data across computations. This models reuse across cells within one named assembly, not retention of that cache across MassForm::assemble calls. Geometry and canonical quadrature caches are primed in both scopes. Mesh/space construction, the scalar oracle and numerical checks are untimed; scatter, constraints, solving and process-first geometry are not measured.

Reference-cache payload is a source-derived model, not measured resident memory. Degrees one through three bound this initial profiling matrix; the high-degree component-expanded cache is investigated separately before launching its multi-gigabyte configurations. Point cases are structural counting-measure operations, not refinement studies. Empty shapes, mixed degrees, other space families and curved/embedded cells are separate scopes.

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

RodinNamedMassKernelBenchmarks · auto · regular · ranks: 1