Zero-allocation tangent for ViscousPolyconvex

[miguelmaso]

Add generated implementations of - (binary and unary) for TensorValue, mirroring the existing +. Without them, subtraction of fourth-order tensors fell back to the generic Gridap implementation, which exceeds Julia's inlining threshold for TensorValue{9,9} and heap-allocates the result.

Those subtractions appear in ∂Sv∂C_Cᵥfix and ∂Cv⁻¹∂C, i.e. exactly on the path of the viscoelastic tangent operator, which is why only ∂∂Ψ∂FF allocated while Ψ and ∂Ψ∂F did not.

+ is also generalized from TensorValue{D,D} to TensorValue{D1,D2} so that non-square tensors are covered as well. No change in the mathematics.

The three methods build the result with an explicit element type, which also covers empty tensors: Gridap builds TensorValue{0,3} values when it writes the vertex grid of a 3D model, and leaving the type implicit made them throw UndefVarError: T not defined, breaking writevtk(model) for any code that loads HyperFEM. The price of fixing the element type with promote_type is that adding two Bool tensors now errors instead of promoting to Int as Gridap does; the tensors involved in a finite element evaluation are floating point.

Visco-polyconvex ∂∂Ψ∂FF: 187 allocs / 15552 B / 5367 ns -> 0 allocs / 0 B / 599 ns.
Visco-elastic ∂∂Ψ∂FF: 1021 allocs / 49600 ns -> 501 allocs / 34200 ns.

Also interpolate the arguments of the tensor algebra benchmarks. Without $, the benchmarked expressions read non-const globals, so the call is dynamically dispatched and the result is boxed: this is the source of the spurious "1 alloc of 0.656 kB" reported for IIsym, push_forward_C_to_F and ×ᵢ⁴, which are already allocation-free.

See #231

[miguelmaso]

#232 is fixing the issues introduced by #231: breaking writevtk due to type pyracy

⚠️⚠️Type piracy must be addressed⚠️⚠️

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	main	d25fca3...	main / d25fca3...
Constitutive models/Visco-elastic Ψ	0.0379 ± 0.0058 ms	18.4 ± 7.5 μs	2.06 ± 0.89
Constitutive models/Visco-elastic ∂Ψ∂F	0.0445 ± 0.0074 ms	25.2 ± 8.9 μs	1.77 ± 0.69
Constitutive models/Visco-elastic ∂∂Ψ∂FF	0.0785 ± 0.021 ms	0.0514 ± 0.016 ms	1.53 ± 0.63
Constitutive models/Visco-polyconvex Ψ	0.161 ± 0.01 μs	0.16 ± 0.001 μs	1.01 ± 0.063
Constitutive models/Visco-polyconvex ∂Ψ∂F	0.181 ± 0.01 μs	0.19 ± 0.001 μs	0.953 ± 0.053
Constitutive models/Visco-polyconvex ∂∂Ψ∂FF	11.2 ± 5.6 μs	0.781 ± 0.011 μs	14.3 ± 7.2
Simulations/StaticMechanicalDirichlet	0.155 ± 0.0073 s	0.161 ± 0.0097 s	0.965 ± 0.074
Simulations/StaticMechanicalNeumann	0.122 ± 0.013 s	0.126 ± 0.016 s	0.968 ± 0.16
Simulations/ViscoElastic	10.3 s	7.29 s	1.41
Tensor algebra/Cofactor	0.07 ± 0.01 μs	0.08 ± 0 μs	0.875 ± 0.12
Tensor algebra/Det(A)Inv(A')	0.1 ± 0.01 μs	0.12 ± 0.011 μs	0.833 ± 0.11
Tensor algebra/IIsym	0.06 ± 0.01 μs	0.06 ± 0 μs	1 ± 0.17
Tensor algebra/push_forward_C_to_F	0.27 ± 0.019 μs	0.211 ± 0.011 μs	1.28 ± 0.11
Tensor algebra/×ᵢ⁴	0.051 ± 0.01 μs	0.06 ± 0 μs	0.85 ± 0.17
Tensor algebra/δδ_λ_2d	20 ± 10 ns	20 ± 10 ns	1 ± 0.71
Tensor algebra/δδ_μ_2d	20 ± 10 ns	20 ± 10 ns	1 ± 0.71
time_to_load	1.96 ± 0.0092 s	2.03 ± 0.0093 s	0.966 ± 0.0063

Memory benchmarks

	main	d25fca3...	main / d25fca3...
Constitutive models/Visco-elastic Ψ	0.56 k allocs: 0.044 MB	0.212 k allocs: 26.8 kB	1.68
Constitutive models/Visco-elastic ∂Ψ∂F	0.609 k allocs: 0.0489 MB	0.261 k allocs: 31.7 kB	1.58
Constitutive models/Visco-elastic ∂∂Ψ∂FF	1.03 k allocs: 0.0829 MB	0.508 k allocs: 0.0573 MB	1.45
Constitutive models/Visco-polyconvex Ψ	0 allocs: 0 B	0 allocs: 0 B
Constitutive models/Visco-polyconvex ∂Ψ∂F	0 allocs: 0 B	0 allocs: 0 B
Constitutive models/Visco-polyconvex ∂∂Ψ∂FF	0.187 k allocs: 15.2 kB	0 allocs: 0 B
Simulations/StaticMechanicalDirichlet	1.51 M allocs: 0.108 GB	1.51 M allocs: 0.108 GB	1
Simulations/StaticMechanicalNeumann	1.47 M allocs: 0.0922 GB	1.47 M allocs: 0.0922 GB	1
Simulations/ViscoElastic	0.16 G allocs: 12.5 GB	0.0801 G allocs: 8.52 GB	1.46
Tensor algebra/Cofactor	2 allocs: 0.156 kB	2 allocs: 0.156 kB	1
Tensor algebra/Det(A)Inv(A')	4 allocs: 0.25 kB	4 allocs: 0.25 kB	1
Tensor algebra/IIsym	1 allocs: 0.656 kB	1 allocs: 0.656 kB	1
Tensor algebra/push_forward_C_to_F	1 allocs: 0.656 kB	1 allocs: 0.656 kB	1
Tensor algebra/×ᵢ⁴	1 allocs: 0.656 kB	1 allocs: 0.656 kB	1
Tensor algebra/δδ_λ_2d	0 allocs: 0 B	0 allocs: 0 B
Tensor algebra/δδ_μ_2d	0 allocs: 0 B	0 allocs: 0 B
time_to_load	0.205 k allocs: 11.9 kB	0.205 k allocs: 11.9 kB	1