Custom kernels
When defining your own kernels, there is one required as well as some optional methods to overload in order to provide kernel-specific information to the constructor. The table below summarizes the interface methods, where Y is a SourceTree object, x is an SVector representing a point, and K is your custom kernel:
| Method's name | Required | Brief description |
|---|---|---|
wavenumber(K) | Yes | Return the wavenumber of your kernel |
return_type(K) (@ref) | No | Type of element returned by K(x,y) |
centered_factor(K,x,Y) | No | A representative value of K(x,y) for y ∈ Y |
inv_centered_factor(K,x,Y) | No | A representative value of inv(K(x,y)) for y ∈ Y |
transfer_factor(K,x,Y) | No | Transfer function given by inv_centered_factor(K,x,parent(Y))*centered_factor(K,x,Y) |
near_interaction!(C,K,X,Y,σ,I,J) | No | Compute C[i] <- C[i] + ∑ⱼ K(X[i],Y[j])*σ[j] for i ∈ I, j ∈ J |
Because the IFGF algorithms must adapt its interpolation scheme depending on the frequency of oscillations to control the interpolation error, you must extend the IFGF.wavenumber method. If the kernel is not oscillatory (e.g. exponential kernel, Newtonian potential), simply return 0.
The centered_factor, inv_centered_factor, and transfer_factor have reasonable defaults, and typically are overloaded only for performance reasons (e.g. if some analytic simplifications are available).
Finally, the near_interaction method is called at the leaves of the source tree to compute the near interactions. Extending this function to make use of e.g. SIMD instructions can significantly speed up some parts of the code.