[alexfikl]

This implements rewriting a target kernel (e.g. Stokeslet) in terms of a base kernel (e.g. biharmonic) as a linear constant-coefficient combination of derivatives.

Currently, it just hoists get_deriv_relation_kernel from inducer/pytential#162 with some minimal changes:

• Clean up the retry logic for the LU factorization.
• Add a loop on the max order of derivatives.

TODO:

• Make sure the LU based decomposition works the same as before.
• Add a bunch of tests for it (based on the tests in pytential).
• Implement a hopefully better (but likely slower?) purely-symbolic version.
  • Implemented a faster Fourier-based thing instead. It only works with fundamental solutions though (i.e. Stokeslet, but not Stresslet)
• Hook into documentation.

Needs

• Use SpatialConstant naming in get_pde_as_diff_op #309

cc @isuruf

[Copilot]

🟡 Changes recommended

Unresolved fallback failures, rejected constant-only rewrites, and parameter-symbol mismatches break supported behavior and existing tests.

5 open findings

• Use prefixed spatial constants in PDE substitutions · New
• Pass inner target kernel to the default LU fallback · New
• Convert unavailable scalar PDE errors to RewriteFailedError · New
• Preserve constant-only LU rewrite coefficients · New
• Avoid double-prefixing Yukawa parameter names · New

What changed in this PR

Adds kernel rewriting to express target kernels as constant-coefficient combinations of base-kernel derivatives.

Changes:

• Implements symbolic Fourier and numerical LU rewriting.
• Standardizes spatial-constant parameters in kernel PDEs.
• Adds rewrite tests and documentation.

File	Description
sumpy/​tools.py	Adds multi-index differentiation.
sumpy/​test/​test_misc.py	Updates PDE tests for spatial constants.
sumpy/​test/​test_kernel_rewrite.py	Adds rewriting and conditioning tests.
sumpy/​kernel.py	Updates PDE parameters and marks unsupported system PDEs.
sumpy/​kernel_rewrite.py	Implements rewrite representations and algorithms.
doc/​kernel.rst	Includes kernel rewriting documentation.
.basedpyright/​baseline.json	Updates type-checking diagnostics.

🧠 Review effort: Balanced

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[alexfikl]

Not sure we want to support that.

[inducer]

kernel and base_kernel?

[alexfikl]

Done in f57077c.