[ShawnL00]

This adds ODELineTaylorLocalExpansion for direct QBX evaluation of kernels of the form $G(z) = g(q)$, where
$q = |z|^2$. It derives an ODE for $g$ from the kernel’s PDE and uses it to construct a recurrence for the line Taylor expansions.

• Supported base kernels include Laplace, Helmholtz, Yukawa, and biharmonic kernels in 2D and 3D.
• Linear combinations of source and target operators that share the same base kernel are supported.

One example:

base_kernel = LaplaceKernel(3)

source_kernels = (
    base_kernel,
    *(AxisSourceDerivative(axis, base_kernel) for axis in range(3)),
)
target_kernels = (
    base_kernel,
    AxisTargetDerivative(0, base_kernel),
)

expansion = ODELineTaylorLocalExpansion(
    base_kernel, order=8, target_kernels=target_kernels)

lpot = LayerPotential(
    expansion=expansion,
    target_kernels=target_kernels,
    source_kernels=source_kernels)

The existing QBX, jump-relation, target-derivative, and matrix-generation tests now include the new expansion. Additional circle tests cover the biharmonic single layer and Laplace hypersingular operator.

Todo:

• Support matrix kernels.
• Support operators involving multiple base kernels.
• Automatically reduce the ODE order when possible, e.g., using a lower-order ODE for biharmonic kernels.
• Support for user-supplied ODEs.
• Extend the recurrence to mixed-derivative expansions for FMM support.