Module: src/physics/database Purpose: Index of documentation for BELFEM's precomputed lookup-table module

Overview

The database module turns an expensive property function into a cheap one. A property is sampled once onto a structured tensor grid, projected onto a smooth basis, stored, and thereafter read by shape-function interpolation — so the cost is paid at setup instead of at every quadrature point of every Newton iteration.

Its principal consumer is physics/materials, where the field- and temperature-dependent resistivity of normal metals is served from such a table.

Documents

Document	Read it for
database_usage_guide.md	what the module is, how to build and query a table, why the projection step exists, the parallel contract, and the consumer pitfalls

Quick Reference

Class	File	Role
Database	cl_Database.hpp / .cpp	holds the finished table; evaluate, evaluate_deriv{x,y,z}, min, max, save
database::Projector	cl_DatabaseProjector.hpp / .cpp	build-time only: L2-projects sampled values onto a B-spline basis and returns node values

Question	Answer
Why project at all, instead of storing the samples?	so the derivative accessors return a continuous field — raw Lagrange interpolation of samples is only C⁰, and its jumps degrade Newton tangents
Is the build parallel?	the call is collective, the work is not — rank 0 builds, all ranks receive
Which solver?	compile-time preference MUMPS → PARDISO → SUPERLU → UMFPACK; STRUMPACK deliberately excluded (matrices too small)
Who clamps the query to the grid?	the caller, always

Development Notes

The mesh constructor requires a tensor mesh; it checks is_tensormesh() and raises BELFEM_ERROR otherwise.
Stored values may be a transformed quantity (materials store log(rho)) — undo the transform on the way out, and remember a stored derivative is the derivative of the transform.
Rebuilt tables agree bit-for-bit only single-threaded; multithreaded solves carry ordinary reassociation noise of order 1e-7 relative.
Saved HDF5 records carry no format-version stamp, so a caching consumer must probe for an expected dataset before trusting a file on disk.