Stokes biharmonic

[isuruf]

Mirror of https://gitlab.tiker.net/inducer/pytential/-/merge_requests/163 for review

[inducer]

When I print the expression you feed to bind(), there's a "naked" (i.e. not inside an IntG) area element there:

CSE0 : sigma[0] + (-1)*(NodeSum(area_element*w_quad[?]*sigma[0]) / area)
CSE1 : sigma[1] + (-1)*(NodeSum(area_element*w_quad[?]*sigma[1]) / area)
area : NodeSum(area_element*w_quad[?]*Ones[?])
area_element : sqrt(pd_matrix0_0*pd_matrix0_0 + pd_matrix1_0*pd_matrix1_0)
pd_matrix0_0 : d/dr0[?] x0[?]
pd_matrix1_0 : d/dr0[?] x1[?]
===========================================================================
array(
  0: (-1)*(Int[?->?]@(2){mu: mu} (StressletKnl2D_000 * normal[0]*sigma[0]) + Int[?->?]@(2){mu: mu} (StressletKnl2D_001 * normal[0]*sigma[1]) + Int[?->?]@(2){mu: mu} (StressletKnl2D_001 * normal[1]*sigma[0]) + Int[?->?]@(2){mu: mu} (StressletKnl2D_011 * normal[1]*sigma[1])) + (-1)*((-1) / mu)*(Int[?->?]@(2) (d/dx1 d/dx1 BiharmKnl2D * CSE0) + (-0.1193662073189215)*CSE0) + ((-1) / mu)*Int[?->?]@(2) (d/dx1 d/dx0 BiharmKnl2D * CSE1) + (-1)*((-1)*((-1) / mu)*(Int[?->?]@(2) (d/dx1 d/dx1 BiharmKnl2D * omega[0]) + (-0.1193662073189215)*omega[0]) + ((-1) / mu)*Int[?->?]@(2) (d/dx1 d/dx0 BiharmKnl2D * omega[1])) + sigma_int_val[0]
  ---------------------------------------------------------------------------
  1: (-1)*(Int[?->?]@(2){mu: mu} (StressletKnl2D_001 * normal[0]*sigma[0]) + Int[?->?]@(2){mu: mu} (StressletKnl2D_011 * normal[0]*sigma[1]) + Int[?->?]@(2){mu: mu} (StressletKnl2D_011 * normal[1]*sigma[0]) + Int[?->?]@(2){mu: mu} (StressletKnl2D_111 * normal[1]*sigma[1])) + ((-1) / mu)*Int[?->?]@(2) (d/dx0 d/dx1 BiharmKnl2D * CSE0) + (-1)*((-1) / mu)*(Int[?->?]@(2) (d/dx0 d/dx0 BiharmKnl2D * CSE1) + (-0.1193662073189215)*CSE1) + (-1)*(((-1) / mu)*Int[?->?]@(2) (d/dx0 d/dx1 BiharmKnl2D * omega[0]) + (-1)*((-1) / mu)*(Int[?->?]@(2) (d/dx0 d/dx0 BiharmKnl2D * omega[1]) + (-0.1193662073189215)*omega[1])) + sigma_int_val[1]
)

(Use sym.pretty() to reproduce this.)
Specifically, I'm talking about theCSE0. Since that's outside an IntG, it's evaluated in a "target" context. The target you request are the vis points, and it's not possible/not reasonable to calculate derivatives on them (in order to compute an area element), and so it yells at you.

[isuruf]

Got it. Thanks. Is there a way to pass a constant to IntG instead of a sumpy kernel?

[isuruf]

I meant passing CSE0 like IntG(1, density=CSE0)

[inducer]

Got it. Thanks. Is there a way to pass a constant to IntG instead of a sumpy kernel?

I mean, you could create an ExpressionKernel with expression 1. But it's probably overkill to warm up the layer potential machinery for that. What you want is probably a length integral times the constant. (sym.integral) The ToTargetTagger likely won't auto-tag this correctly, so you'll have to manually pass it the name of the source geometry.

[isuruf]

@inducer, is this correct?

[inducer]

Yes, it looks that way. One remaining issue is that the Stokeslet is being passed a density with the mean removed. This mean also involves an integral that needs to be told where to evaluate. I'm suspecting there might be a way to make the ToTargetTagger smarter to automatically tag things more appropriately.

[inducer]

Raise a DeprecationWarning, remove from docs.

[inducer]

Underscore me.

[inducer]

What are u_i in these docstrings?

[alexfikl]

Suggested change

	return 1, int_g
	return int_g

?