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WADG should use overintegration #173

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inducer opened this issue Oct 12, 2021 · 2 comments
Open

WADG should use overintegration #173

inducer opened this issue Oct 12, 2021 · 2 comments
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@inducer
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inducer commented Oct 12, 2021

@thomasgibson pointed out that our WADG could/should be able to take advantage of overintegration, which it currently doesn't. Consider the matrix we're supposed to apply:

image

(From the paper) Consider the current implementation:

grudge/grudge/op.py

Lines 645 to 653 in 2af3528

group_data.append(
# Based on https://arxiv.org/pdf/1608.03836.pdf
# true_Minv ~ ref_Minv * ref_M * (1/jac_det) * ref_Minv
actx.einsum("ei,ij,ej->ei",
jac_inv,
ref_mass_inverse,
vec_i,
tagged=(FirstAxisIsElementsTag(),))
)

The ref_Minv * ref_M * (1/jac_det) * ref_Minv * u shold really be (in weird pseudocode):

ref_Minv * ref_M("overintegrated") * (1/project("overintegrated", jac_det) * project("overintegrated", ref_Minv * u)

cc @lukeolson

@thomasgibson thomasgibson self-assigned this Oct 12, 2021
@inducer
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inducer commented May 24, 2024

cc @MTCam

Newly relevant for quads.

@inducer
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inducer commented May 24, 2024

Though in the long run we should probably switch to mass lumping, which is cheaper.

Made a separate issue for the mass-lumped inverse: #343.

cc @a-alveyblanc

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