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	0.0446 ± 0.0057 ms	22 ± 9.3 μs	2.02 ± 0.9
Constitutive models/Visco-elastic ∂Ψ∂F	0.0543 ± 0.019 ms	0.0321 ± 0.012 ms	1.69 ± 0.86
Constitutive models/Visco-elastic ∂∂Ψ∂FF	0.0968 ± 0.032 ms	0.0657 ± 0.022 ms	1.47 ± 0.69
Constitutive models/Visco-polyconvex Ψ	0.19 ± 0.001 μs	0.191 ± 0.01 μs	0.995 ± 0.052
Constitutive models/Visco-polyconvex ∂Ψ∂F	0.2 ± 0.009 μs	0.21 ± 0.001 μs	0.952 ± 0.043
Constitutive models/Visco-polyconvex ∂∂Ψ∂FF	12.1 ± 6.1 μs	0.792 ± 0.001 μs	15.3 ± 7.7
Simulations/StaticMechanicalDirichlet	0.18 ± 0.0051 s	0.18 ± 0.0052 s	1 ± 0.041
Simulations/StaticMechanicalNeumann	0.147 ± 0.011 s	0.148 ± 0.011 s	0.995 ± 0.1
Simulations/ViscoElastic	12.2 s	8.55 s	1.42
Tensor algebra/Cofactor	0.08 ± 0.01 μs	0.071 ± 0.01 μs	1.13 ± 0.21
Tensor algebra/Det(A)Inv(A')	0.11 ± 0.02 μs	0.111 ± 0.02 μs	0.991 ± 0.25
Tensor algebra/IIsym	0.07 ± 0 μs	0.08 ± 0.01 μs	0.875 ± 0.11
Tensor algebra/push_forward_C_to_F	0.3 ± 0.01 μs	0.301 ± 0.001 μs	0.997 ± 0.033
Tensor algebra/×ᵢ⁴	0.06 ± 0.01 μs	0.07 ± 0.01 μs	0.857 ± 0.19
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	2.31 ± 0.015 s	2.31 ± 0.021 s	1 ± 0.011

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	0.205 k allocs: 11.9 kB	0.201 k allocs: 11.8 kB	1.02

[miguelmaso]

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

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

• ∂Ψ∂F: 160x
• ∂∂Ψ∂FF: 100x