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.

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.

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	main	7052793...	main / 7052793...
Constitutive models/Visco-elastic Ψ	0.0476 ± 0.0062 ms	23.8 ± 10 μs	2 ± 0.88
Constitutive models/Visco-elastic ∂Ψ∂F	0.0556 ± 0.01 ms	0.0323 ± 0.013 ms	1.72 ± 0.74
Constitutive models/Visco-elastic ∂∂Ψ∂FF	0.0986 ± 0.035 ms	0.0654 ± 0.023 ms	1.51 ± 0.74
Constitutive models/Visco-polyconvex Ψ	0.2 ± 0.01 μs	0.2 ± 0.01 μs	1 ± 0.071
Constitutive models/Visco-polyconvex ∂Ψ∂F	0.201 ± 0.01 μs	0.201 ± 0.01 μs	1 ± 0.07
Constitutive models/Visco-polyconvex ∂∂Ψ∂FF	13.6 ± 7.1 μs	0.781 ± 0.01 μs	17.5 ± 9.1
Simulations/StaticMechanicalDirichlet	0.188 ± 0.009 s	0.187 ± 0.0084 s	1 ± 0.066
Simulations/StaticMechanicalNeumann	0.15 ± 0.015 s	0.151 ± 0.016 s	0.987 ± 0.15
Simulations/ViscoElastic	12.3 s	8.54 s	1.44
Tensor algebra/Cofactor	0.08 ± 0 μs	0.08 ± 0 μs	1 ± 0
Tensor algebra/Det(A)Inv(A')	0.13 ± 0.03 μs	0.12 ± 0.021 μs	1.08 ± 0.31
Tensor algebra/IIsym	0.08 ± 0.001 μs	0.07 ± 0.001 μs	1.14 ± 0.022
Tensor algebra/push_forward_C_to_F	0.28 ± 0.001 μs	0.281 ± 0.01 μs	0.996 ± 0.036
Tensor algebra/×ᵢ⁴	0.07 ± 0.01 μs	0.07 ± 0 μs	1 ± 0.14
Tensor algebra/δδ_λ_2d	30 ± 0 ns	30 ± 0 ns	1 ± 0
Tensor algebra/δδ_μ_2d	30 ± 0 ns	30 ± 0 ns	1 ± 0
time_to_load	2.41 ± 0.0017 s	2.43 ± 0.0085 s	0.992 ± 0.0035

Memory benchmarks

	main	7052793...	main / 7052793...
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	0.201 k allocs: 11.8 kB	0.215 k allocs: 12.4 kB	0.951

[miguelmaso]

The ViscousPolyconvex model takes exactly 0 alloc!!!!!

Speed-up with respect to ViscousIncompressible at Gauss point evaluation:

• ∂Ψ∂F: 160x
• ∂∂Ψ∂FF: 100x