3. Nonlinear Elasticity#
from ngsolve import *
from ngsolve.webgui import Draw
a rectangle with refinement at corners:
from netgen.occ import *
shape = Rectangle(1,0.1).Face()
shape.edges.Max(X).name="right"
shape.edges.Min(X).name="left"
shape.edges.Max(Y).name="top"
shape.edges.Min(Y).name="bot"
shape.vertices.Min(X+Y).maxh=0.01
shape.vertices.Min(X-Y).maxh=0.01
mesh = Mesh(OCCGeometry(shape, dim=2).GenerateMesh(maxh=0.05))
Cauchy-Green tensor
\[
C = F^T F \qquad \text{with} \qquad F = I + \nabla u
\]
and hyperelastic energy density
\[
W : {\mathbb R}^{d \times d, sym} \rightarrow {\mathbb R}
\]
E, nu = 210, 0.2
mu = E / 2 / (1+nu)
lam = E * nu / ((1+nu)*(1-2*nu))
def C(u):
F = Id(2) + Grad(u)
return F.trans * F
def NeoHooke (C):
return 0.5*mu*(Trace(C-Id(2)) + 2*mu/lam*Det(C)**(-lam/2/mu)-1)
stationary point of total energy:
\[
\delta \int W(C(u)) - f u = 0
\]
factor = Parameter(0)
force = CoefficientFunction( (0,factor) )
fes = H1(mesh, order=4, dirichlet="left", dim=mesh.dim)
u = fes.TrialFunction()
a = BilinearForm(fes, symmetric=True)
a += Variation(NeoHooke(C(u)).Compile()*dx)
a += Variation((-InnerProduct(force,u)).Compile()*dx)
gfu = GridFunction(fes)
gfu.vec[:] = 0
a simple Newton solver, using automatic differentiation for residual and tangential stiffness:
def SolveNewton(printrates=False):
for it in range(10):
if (printrates):
print ("it", it, "energy = ", a.Energy(gfu.vec))
res = a.Apply(gfu.vec)
a.AssembleLinearization(gfu.vec)
inv = a.mat.Inverse(fes.FreeDofs() )
gfu.vec.data -= inv*res
factor.Set(0.4)
SolveNewton(printrates=True)
scene = Draw (C(gfu)[0,0]-1, mesh, deformation=gfu, min=-0.1, max=0.1, center=(0.5,0.5))
it 0 energy = 8.749999999999972
it 1 energy = 8.81117555553033
it 2 energy = 8.748116767901411
it 3 energy = 8.747829234576706
it 4 energy = 8.74782915372321
it 5 energy = 8.747829153708558
it 6 energy = 8.747829153708558
it 7 energy = 8.747829153708558
it 8 energy = 8.747829153708558
it 9 energy = 8.747829153708558
numsteps = 5
maxload = 2
for ls in range (numsteps):
factor.Set(maxload*(ls+1)/numsteps)
SolveNewton()
Draw (C(gfu)[0,0]-1, mesh, deformation=gfu, min=-0.2, max=0.2)
3.1. Stress tensor#
Compute \(2^{nd}\) Piola Kirchhoff stress tensor by symbolic differentiation:
\[
\Sigma_{i,j} = \frac{\partial W}{\partial C_{i,j}} (C)
\]
C_=C(gfu).MakeVariable()
sigma = NeoHooke(C_).Diff(C_)
Draw (sigma[0,0], mesh, "Sxx", deformation=gfu, min=-10.001, max=10.001);
The energy functional is represented as an expression tree:
u = fes.TrialFunction()
print (NeoHooke(C(u)))
43.75*(coef binary operation '-', real
coef binary operation '+', real
coef trace, real
coef binary operation '-', real, dims = 2 x 2
coef matrix-matrix multiply, real, dims = 2 x 2
coef Matrix transpose, real, dims = 2 x 2
coef binary operation '+', real, dims = 2 x 2
coef Identity matrix, real, dims = 2 x 2
coef trial-function diffop = grad, real, dims = 2 x 2
coef binary operation '+', real, dims = 2 x 2
coef Identity matrix, real, dims = 2 x 2
coef trial-function diffop = grad, real, dims = 2 x 2
coef Identity matrix, real, dims = 2 x 2
coef scale 3, real
coef binary operation 'pow', real
coef binary operation '*', real
coef Determinant, real
coef binary operation '+', real, dims = 2 x 2
coef Identity matrix, real, dims = 2 x 2
coef trial-function diffop = grad, real, dims = 2 x 2
coef Determinant, real
coef binary operation '+', real, dims = 2 x 2
coef Identity matrix, real, dims = 2 x 2
coef trial-function diffop = grad, real, dims = 2 x 2
coef -0.333333, real
coef 1, real
)
With the Compile method, the tree is linearized, and common sub-expressions are merged:
print (NeoHooke(C(u)).Compile())
Compiled CF:
Step 0: Identity matrix, dims = 2 x 2
Step 1: trial-function diffop = grad, dims = 2 x 2
Step 2: binary operation '+', dims = 2 x 2
input: 0 1
Step 3: Matrix transpose, dims = 2 x 2
input: 2
Step 4: matrix-matrix multiply, dims = 2 x 2
input: 3 2
Step 5: Identity matrix, dims = 2 x 2
Step 6: binary operation '-', dims = 2 x 2
input: 4 5
Step 7: trace
input: 6
Step 8: Determinant
input: 2
Step 9: binary operation '*'
input: 8 8
Step 10: -0.333333
Step 11: binary operation 'pow'
input: 9 10
Step 12: scale 3
input: 11
Step 13: binary operation '+'
input: 7 12
Step 14: 1
Step 15: binary operation '-'
input: 13 14
Step 16: scale 43.75
input: 15
We can also real-compile, what means we generate C++ code, and send it through the compiler
ngsglobals.msg_level=3
NeoHooke(C(u)).Compile(realcompile=True, wait=True, keep_files=True);
Compiled CF:
N5ngfem27IdentityCoefficientFunctionE
N5ngfem13ProxyFunctionE
N5ngfem13cl_BinaryOpCFINS_11GenericPlusEEE
N5ngfem28TransposeCoefficientFunctionE
N5ngfem29MultMatMatCoefficientFunctionE
N5ngfem27IdentityCoefficientFunctionE
N5ngfem13cl_BinaryOpCFINS_12GenericMinusEEE
N5ngfem24TraceCoefficientFunctionE
N5ngfem30DeterminantCoefficientFunctionILi2EEE
N5ngfem13cl_BinaryOpCFINS_11GenericMultEEE
N5ngfem27ConstantCoefficientFunctionE
N5ngfem13cl_BinaryOpCFI10GenericPowEE
N5ngfem24ScaleCoefficientFunctionE
N5ngfem13cl_BinaryOpCFINS_11GenericPlusEEE
N5ngfem27ConstantCoefficientFunctionE
N5ngfem13cl_BinaryOpCFINS_12GenericMinusEEE
N5ngfem24ScaleCoefficientFunctionE
inputs =
0:
1:
2: 0 1
3: 2
4: 3 2
5:
6: 4 5
7: 6
8: 2
9: 8 8
10:
11: 9 10
12: 11
13: 7 12
14:
15: 13 14
16: 15
Compiled CF:
step 0: N5ngfem27IdentityCoefficientFunctionE
step 1: N5ngfem13ProxyFunctionE
step 2: N5ngfem13cl_BinaryOpCFINS_11GenericPlusEEE
step 3: N5ngfem28TransposeCoefficientFunctionE
step 4: N5ngfem29MultMatMatCoefficientFunctionE
step 5: N5ngfem27IdentityCoefficientFunctionE
step 6: N5ngfem13cl_BinaryOpCFINS_12GenericMinusEEE
step 7: N5ngfem24TraceCoefficientFunctionE
step 8: N5ngfem30DeterminantCoefficientFunctionILi2EEE
step 9: N5ngfem13cl_BinaryOpCFINS_11GenericMultEEE
step 10: N5ngfem27ConstantCoefficientFunctionE
step 11: N5ngfem13cl_BinaryOpCFI10GenericPowEE
step 12: N5ngfem24ScaleCoefficientFunctionE
step 13: N5ngfem13cl_BinaryOpCFINS_11GenericPlusEEE
step 14: N5ngfem27ConstantCoefficientFunctionE
step 15: N5ngfem13cl_BinaryOpCFINS_12GenericMinusEEE
step 16: N5ngfem24ScaleCoefficientFunctionE
compiling...
compiling...
linking...
done
keeping generated files at /var/folders/_l/x5rb66s96zd96123z8dzgl5r0000gn/T/ngsolve_tmp_0_0_sMlnBL
The generated code:
#include<fem.hpp>
#if defined(__GNUC__) || defined(__clang__)
#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
#endif
using namespace ngfem;
extern "C" {
extern "C" void* compiled_code_pointer48;
extern "C" void* compiled_code_pointer49;
extern "C" void* compiled_code_pointer50;
extern "C" void* compiled_code_pointer51;
extern "C" void* compiled_code_pointer52;
extern "C" void* compiled_code_pointer53;
void CompiledEvaluate(BaseMappedIntegrationRule & mir, BareSliceMatrix<double> results ) {
FlatMatrix<double> values_1;
ProxyUserData * tmp_1_0 = (ProxyUserData*)mir.GetTransformation().userdata;
{
if (tmp_1_0->fel) {
auto x = tmp_1_0->GetMemory (reinterpret_cast<ProxyFunction*>(compiled_code_pointer48));
values_1.AssignMemory(x.Height(), x.Width(), &x(0,0));
}
}
[[maybe_unused]] const bool has_values_1 = tmp_1_0->HasMemory(reinterpret_cast<ProxyFunction*>(compiled_code_pointer48));
double comp_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==0 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer48))
comp_1_0_0 = 1.0;
double comp_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==1 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer48))
comp_1_0_1 = 1.0;
double comp_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==2 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer48))
comp_1_1_0 = 1.0;
double comp_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==3 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer48))
comp_1_1_1 = 1.0;
[[maybe_unused]] auto points = mir.GetPoints();
[[maybe_unused]] auto domain_index = mir.GetTransformation().GetElementIndex();
for ( auto i : Range(mir)) {
[[maybe_unused]] auto & ip = mir[i];
// step 0: Identity matrix
double var_0_0_0;
double var_0_0_1;
double var_0_1_0;
double var_0_1_1;
var_0_0_0 = 1.0;
var_0_0_1 = 0.0;
var_0_1_0 = 0.0;
var_0_1_1 = 1.0;
// step 1: trial-function diffop = grad
double var_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_0 = 0.0;
double var_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_1 = 0.0;
double var_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_0 = 0.0;
double var_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_1 = 0.0;
if (has_values_1) {
var_1_0_0 = values_1(i,0);
var_1_0_1 = values_1(i,1);
var_1_1_0 = values_1(i,2);
var_1_1_1 = values_1(i,3);
}
// step 2: binary operation '+'
double var_2_0_0;
double var_2_0_1;
double var_2_1_0;
double var_2_1_1;
var_2_0_0 = var_0_0_0 + var_1_0_0;
var_2_0_1 = var_0_0_1 + var_1_0_1;
var_2_1_0 = var_0_1_0 + var_1_1_0;
var_2_1_1 = var_0_1_1 + var_1_1_1;
// step 3: Matrix transpose
double var_3_0_0;
double var_3_0_1;
double var_3_1_0;
double var_3_1_1;
var_3_0_0 = var_2_0_0;
var_3_0_1 = var_2_1_0;
var_3_1_0 = var_2_0_1;
var_3_1_1 = var_2_1_1;
// step 4: matrix-matrix multiply
double var_4_0_0;
double var_4_0_1;
double var_4_1_0;
double var_4_1_1;
var_4_0_0 = (((var_3_0_0 * var_2_0_0)) + (var_3_0_1 * var_2_1_0));
var_4_0_1 = (((var_3_0_0 * var_2_0_1)) + (var_3_0_1 * var_2_1_1));
var_4_1_0 = (((var_3_1_0 * var_2_0_0)) + (var_3_1_1 * var_2_1_0));
var_4_1_1 = (((var_3_1_0 * var_2_0_1)) + (var_3_1_1 * var_2_1_1));
// step 5: Identity matrix
double var_5_0_0;
double var_5_0_1;
double var_5_1_0;
double var_5_1_1;
var_5_0_0 = 1.0;
var_5_0_1 = 0.0;
var_5_1_0 = 0.0;
var_5_1_1 = 1.0;
// step 6: binary operation '-'
double var_6_0_0;
double var_6_0_1;
double var_6_1_0;
double var_6_1_1;
var_6_0_0 = var_4_0_0 - var_5_0_0;
var_6_0_1 = var_4_0_1 - var_5_0_1;
var_6_1_0 = var_4_1_0 - var_5_1_0;
var_6_1_1 = var_4_1_1 - var_5_1_1;
// step 7: trace
double var_7;
var_7 = ((var_6_0_0) + var_6_1_1);
// step 8: Determinant
Mat<2,2,double> mat_8;
mat_8(0,0) = var_2_0_0;
mat_8(0,1) = var_2_0_1;
mat_8(1,0) = var_2_1_0;
mat_8(1,1) = var_2_1_1;
double var_8;
var_8 = Det(mat_8);
// step 9: binary operation '*'
double var_9;
var_9 = var_8 * var_8;
// step 10: -0.333333
double var_10;
var_10 = -0x1.5555555555556p-2 /* (-3.3333333333333337e-01) */;
// step 11: binary operation 'pow'
double var_11;
var_11 = pow(var_9,var_10);
// step 12: scale 3
double var_12;
var_12 = (0x1.8p+1 /* (3.0000000000000000e+00) */ * var_11);
// step 13: binary operation '+'
double var_13;
var_13 = var_7 + var_12;
// step 14: 1
double var_14;
var_14 = 0x1p+0 /* (1.0000000000000000e+00) */;
// step 15: binary operation '-'
double var_15;
var_15 = var_13 - var_14;
// step 16: scale 43.75
double var_16;
var_16 = (0x1.5ep+5 /* (4.3750000000000000e+01) */ * var_15);
double var_17;
var_17 = var_16;
results(i,0) =var_17;
}
}
void CompiledEvaluateSIMD(SIMD_BaseMappedIntegrationRule & mir, BareSliceMatrix<SIMD<double>> results ) {
FlatMatrix<SIMD<double>> values_1;
ProxyUserData * tmp_1_0 = (ProxyUserData*)mir.GetTransformation().userdata;
{
if (tmp_1_0->fel) {
auto x = tmp_1_0->GetAMemory (reinterpret_cast<ProxyFunction*>(compiled_code_pointer49));
values_1.AssignMemory(x.Height(), x.Width(), &x(0,0));
}
}
[[maybe_unused]] const bool has_values_1 = tmp_1_0->HasMemory(reinterpret_cast<ProxyFunction*>(compiled_code_pointer49));
SIMD<double> comp_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==0 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer49))
comp_1_0_0 = 1.0;
SIMD<double> comp_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==1 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer49))
comp_1_0_1 = 1.0;
SIMD<double> comp_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==2 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer49))
comp_1_1_0 = 1.0;
SIMD<double> comp_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==3 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer49))
comp_1_1_1 = 1.0;
[[maybe_unused]] auto points = mir.GetPoints();
[[maybe_unused]] auto domain_index = mir.GetTransformation().GetElementIndex();
for ( auto i : Range(mir)) {
[[maybe_unused]] auto & ip = mir[i];
// step 0: Identity matrix
SIMD<double> var_0_0_0;
SIMD<double> var_0_0_1;
SIMD<double> var_0_1_0;
SIMD<double> var_0_1_1;
var_0_0_0 = 1.0;
var_0_0_1 = 0.0;
var_0_1_0 = 0.0;
var_0_1_1 = 1.0;
// step 1: trial-function diffop = grad
SIMD<double> var_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_0 = 0.0;
SIMD<double> var_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_1 = 0.0;
SIMD<double> var_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_0 = 0.0;
SIMD<double> var_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_1 = 0.0;
// if (tmp_1_0->fel) {
if (has_values_1) {
var_1_0_0 = values_1(0,i);
var_1_0_1 = values_1(1,i);
var_1_1_0 = values_1(2,i);
var_1_1_1 = values_1(3,i);
}
// step 2: binary operation '+'
SIMD<double> var_2_0_0;
SIMD<double> var_2_0_1;
SIMD<double> var_2_1_0;
SIMD<double> var_2_1_1;
var_2_0_0 = var_0_0_0 + var_1_0_0;
var_2_0_1 = var_0_0_1 + var_1_0_1;
var_2_1_0 = var_0_1_0 + var_1_1_0;
var_2_1_1 = var_0_1_1 + var_1_1_1;
// step 3: Matrix transpose
SIMD<double> var_3_0_0;
SIMD<double> var_3_0_1;
SIMD<double> var_3_1_0;
SIMD<double> var_3_1_1;
var_3_0_0 = var_2_0_0;
var_3_0_1 = var_2_1_0;
var_3_1_0 = var_2_0_1;
var_3_1_1 = var_2_1_1;
// step 4: matrix-matrix multiply
SIMD<double> var_4_0_0;
SIMD<double> var_4_0_1;
SIMD<double> var_4_1_0;
SIMD<double> var_4_1_1;
var_4_0_0 = (((var_3_0_0 * var_2_0_0)) + (var_3_0_1 * var_2_1_0));
var_4_0_1 = (((var_3_0_0 * var_2_0_1)) + (var_3_0_1 * var_2_1_1));
var_4_1_0 = (((var_3_1_0 * var_2_0_0)) + (var_3_1_1 * var_2_1_0));
var_4_1_1 = (((var_3_1_0 * var_2_0_1)) + (var_3_1_1 * var_2_1_1));
// step 5: Identity matrix
SIMD<double> var_5_0_0;
SIMD<double> var_5_0_1;
SIMD<double> var_5_1_0;
SIMD<double> var_5_1_1;
var_5_0_0 = 1.0;
var_5_0_1 = 0.0;
var_5_1_0 = 0.0;
var_5_1_1 = 1.0;
// step 6: binary operation '-'
SIMD<double> var_6_0_0;
SIMD<double> var_6_0_1;
SIMD<double> var_6_1_0;
SIMD<double> var_6_1_1;
var_6_0_0 = var_4_0_0 - var_5_0_0;
var_6_0_1 = var_4_0_1 - var_5_0_1;
var_6_1_0 = var_4_1_0 - var_5_1_0;
var_6_1_1 = var_4_1_1 - var_5_1_1;
// step 7: trace
SIMD<double> var_7;
var_7 = ((var_6_0_0) + var_6_1_1);
// step 8: Determinant
Mat<2,2,SIMD<double>> mat_8;
mat_8(0,0) = var_2_0_0;
mat_8(0,1) = var_2_0_1;
mat_8(1,0) = var_2_1_0;
mat_8(1,1) = var_2_1_1;
SIMD<double> var_8;
var_8 = Det(mat_8);
// step 9: binary operation '*'
SIMD<double> var_9;
var_9 = var_8 * var_8;
// step 10: -0.333333
SIMD<double> var_10;
var_10 = -0x1.5555555555556p-2 /* (-3.3333333333333337e-01) */;
// step 11: binary operation 'pow'
SIMD<double> var_11;
var_11 = pow(var_9,var_10);
// step 12: scale 3
SIMD<double> var_12;
var_12 = (0x1.8p+1 /* (3.0000000000000000e+00) */ * var_11);
// step 13: binary operation '+'
SIMD<double> var_13;
var_13 = var_7 + var_12;
// step 14: 1
SIMD<double> var_14;
var_14 = 0x1p+0 /* (1.0000000000000000e+00) */;
// step 15: binary operation '-'
SIMD<double> var_15;
var_15 = var_13 - var_14;
// step 16: scale 43.75
SIMD<double> var_16;
var_16 = (0x1.5ep+5 /* (4.3750000000000000e+01) */ * var_15);
SIMD<double> var_17;
var_17 = var_16;
results(0,i) =var_17;
}
}
void CompiledEvaluateDeriv(BaseMappedIntegrationRule & mir, BareSliceMatrix<AutoDiff<1,double>> results ) {
FlatMatrix<double> values_1;
ProxyUserData * tmp_1_0 = (ProxyUserData*)mir.GetTransformation().userdata;
{
// if (!tmp_1_0)
// throw Exception ("cannot evaluate ProxyFunction without userdata");
if (tmp_1_0->fel) {
auto x = tmp_1_0->GetMemory (reinterpret_cast<ProxyFunction*>(compiled_code_pointer50));
values_1.AssignMemory(x.Height(), x.Width(), &x(0,0));
}
}
[[maybe_unused]] const bool has_values_1 = tmp_1_0->HasMemory(reinterpret_cast<ProxyFunction*>(compiled_code_pointer50));
AutoDiff<1,double> comp_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==0 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer50))
comp_1_0_0.DValue(0) = 1.0;
AutoDiff<1,double> comp_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==1 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer50))
comp_1_0_1.DValue(0) = 1.0;
AutoDiff<1,double> comp_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==2 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer50))
comp_1_1_0.DValue(0) = 1.0;
AutoDiff<1,double> comp_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==3 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer50))
comp_1_1_1.DValue(0) = 1.0;
[[maybe_unused]] auto points = mir.GetPoints();
[[maybe_unused]] auto domain_index = mir.GetTransformation().GetElementIndex();
for ( auto i : Range(mir)) {
[[maybe_unused]] auto & ip = mir[i];
// step 0: Identity matrix
AutoDiff<1,double> var_0_0_0;
AutoDiff<1,double> var_0_0_1;
AutoDiff<1,double> var_0_1_0;
AutoDiff<1,double> var_0_1_1;
var_0_0_0 = 1.0;
var_0_0_1 = 0.0;
var_0_1_0 = 0.0;
var_0_1_1 = 1.0;
// step 1: trial-function diffop = grad
AutoDiff<1,double> var_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_0 = 0.0;
AutoDiff<1,double> var_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_1 = 0.0;
AutoDiff<1,double> var_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_0 = 0.0;
AutoDiff<1,double> var_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_1 = 0.0;
// if (tmp_1_0->fel) {
if (has_values_1) {
var_1_0_0.Value() = values_1(i,0);
var_1_0_1.Value() = values_1(i,1);
var_1_1_0.Value() = values_1(i,2);
var_1_1_1.Value() = values_1(i,3);
}
{
var_1_0_0.DValue(0) = comp_1_0_0.DValue(0);
var_1_0_1.DValue(0) = comp_1_0_1.DValue(0);
var_1_1_0.DValue(0) = comp_1_1_0.DValue(0);
var_1_1_1.DValue(0) = comp_1_1_1.DValue(0);
}
// step 2: binary operation '+'
AutoDiff<1,double> var_2_0_0;
AutoDiff<1,double> var_2_0_1;
AutoDiff<1,double> var_2_1_0;
AutoDiff<1,double> var_2_1_1;
var_2_0_0 = var_0_0_0 + var_1_0_0;
var_2_0_1 = var_0_0_1 + var_1_0_1;
var_2_1_0 = var_0_1_0 + var_1_1_0;
var_2_1_1 = var_0_1_1 + var_1_1_1;
// step 3: Matrix transpose
AutoDiff<1,double> var_3_0_0;
AutoDiff<1,double> var_3_0_1;
AutoDiff<1,double> var_3_1_0;
AutoDiff<1,double> var_3_1_1;
var_3_0_0 = var_2_0_0;
var_3_0_1 = var_2_1_0;
var_3_1_0 = var_2_0_1;
var_3_1_1 = var_2_1_1;
// step 4: matrix-matrix multiply
AutoDiff<1,double> var_4_0_0;
AutoDiff<1,double> var_4_0_1;
AutoDiff<1,double> var_4_1_0;
AutoDiff<1,double> var_4_1_1;
var_4_0_0 = (((var_3_0_0 * var_2_0_0)) + (var_3_0_1 * var_2_1_0));
var_4_0_1 = (((var_3_0_0 * var_2_0_1)) + (var_3_0_1 * var_2_1_1));
var_4_1_0 = (((var_3_1_0 * var_2_0_0)) + (var_3_1_1 * var_2_1_0));
var_4_1_1 = (((var_3_1_0 * var_2_0_1)) + (var_3_1_1 * var_2_1_1));
// step 5: Identity matrix
AutoDiff<1,double> var_5_0_0;
AutoDiff<1,double> var_5_0_1;
AutoDiff<1,double> var_5_1_0;
AutoDiff<1,double> var_5_1_1;
var_5_0_0 = 1.0;
var_5_0_1 = 0.0;
var_5_1_0 = 0.0;
var_5_1_1 = 1.0;
// step 6: binary operation '-'
AutoDiff<1,double> var_6_0_0;
AutoDiff<1,double> var_6_0_1;
AutoDiff<1,double> var_6_1_0;
AutoDiff<1,double> var_6_1_1;
var_6_0_0 = var_4_0_0 - var_5_0_0;
var_6_0_1 = var_4_0_1 - var_5_0_1;
var_6_1_0 = var_4_1_0 - var_5_1_0;
var_6_1_1 = var_4_1_1 - var_5_1_1;
// step 7: trace
AutoDiff<1,double> var_7;
var_7 = ((var_6_0_0) + var_6_1_1);
// step 8: Determinant
Mat<2,2,AutoDiff<1,double>> mat_8;
mat_8(0,0) = var_2_0_0;
mat_8(0,1) = var_2_0_1;
mat_8(1,0) = var_2_1_0;
mat_8(1,1) = var_2_1_1;
AutoDiff<1,double> var_8;
var_8 = Det(mat_8);
// step 9: binary operation '*'
AutoDiff<1,double> var_9;
var_9 = var_8 * var_8;
// step 10: -0.333333
AutoDiff<1,double> var_10;
var_10 = -0x1.5555555555556p-2 /* (-3.3333333333333337e-01) */;
// step 11: binary operation 'pow'
AutoDiff<1,double> var_11;
var_11 = pow(var_9,var_10);
// step 12: scale 3
AutoDiff<1,double> var_12;
var_12 = (0x1.8p+1 /* (3.0000000000000000e+00) */ * var_11);
// step 13: binary operation '+'
AutoDiff<1,double> var_13;
var_13 = var_7 + var_12;
// step 14: 1
AutoDiff<1,double> var_14;
var_14 = 0x1p+0 /* (1.0000000000000000e+00) */;
// step 15: binary operation '-'
AutoDiff<1,double> var_15;
var_15 = var_13 - var_14;
// step 16: scale 43.75
AutoDiff<1,double> var_16;
var_16 = (0x1.5ep+5 /* (4.3750000000000000e+01) */ * var_15);
AutoDiff<1,double> var_17;
var_17 = var_16;
results(i,0) =var_17;
}
}
void CompiledEvaluateDerivSIMD(SIMD_BaseMappedIntegrationRule & mir, BareSliceMatrix<AutoDiff<1,SIMD<double>>> results ) {
FlatMatrix<SIMD<double>> values_1;
ProxyUserData * tmp_1_0 = (ProxyUserData*)mir.GetTransformation().userdata;
{
if (tmp_1_0->fel) {
auto x = tmp_1_0->GetAMemory (reinterpret_cast<ProxyFunction*>(compiled_code_pointer51));
values_1.AssignMemory(x.Height(), x.Width(), &x(0,0));
}
}
[[maybe_unused]] const bool has_values_1 = tmp_1_0->HasMemory(reinterpret_cast<ProxyFunction*>(compiled_code_pointer51));
AutoDiff<1,SIMD<double>> comp_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==0 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer51))
comp_1_0_0.DValue(0) = 1.0;
AutoDiff<1,SIMD<double>> comp_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==1 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer51))
comp_1_0_1.DValue(0) = 1.0;
AutoDiff<1,SIMD<double>> comp_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==2 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer51))
comp_1_1_0.DValue(0) = 1.0;
AutoDiff<1,SIMD<double>> comp_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(tmp_1_0->trial_comp==3 && tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer51))
comp_1_1_1.DValue(0) = 1.0;
[[maybe_unused]] auto points = mir.GetPoints();
[[maybe_unused]] auto domain_index = mir.GetTransformation().GetElementIndex();
for ( auto i : Range(mir)) {
[[maybe_unused]] auto & ip = mir[i];
// step 0: Identity matrix
AutoDiff<1,SIMD<double>> var_0_0_0;
AutoDiff<1,SIMD<double>> var_0_0_1;
AutoDiff<1,SIMD<double>> var_0_1_0;
AutoDiff<1,SIMD<double>> var_0_1_1;
var_0_0_0 = 1.0;
var_0_0_1 = 0.0;
var_0_1_0 = 0.0;
var_0_1_1 = 1.0;
// step 1: trial-function diffop = grad
AutoDiff<1,SIMD<double>> var_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_0 = 0.0;
AutoDiff<1,SIMD<double>> var_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_1 = 0.0;
AutoDiff<1,SIMD<double>> var_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_0 = 0.0;
AutoDiff<1,SIMD<double>> var_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_1 = 0.0;
// if (tmp_1_0->fel) {
if (has_values_1) {
var_1_0_0.Value() = values_1(0,i);
var_1_0_1.Value() = values_1(1,i);
var_1_1_0.Value() = values_1(2,i);
var_1_1_1.Value() = values_1(3,i);
}
{
var_1_0_0.DValue(0) = comp_1_0_0.DValue(0);
var_1_0_1.DValue(0) = comp_1_0_1.DValue(0);
var_1_1_0.DValue(0) = comp_1_1_0.DValue(0);
var_1_1_1.DValue(0) = comp_1_1_1.DValue(0);
}
// step 2: binary operation '+'
AutoDiff<1,SIMD<double>> var_2_0_0;
AutoDiff<1,SIMD<double>> var_2_0_1;
AutoDiff<1,SIMD<double>> var_2_1_0;
AutoDiff<1,SIMD<double>> var_2_1_1;
var_2_0_0 = var_0_0_0 + var_1_0_0;
var_2_0_1 = var_0_0_1 + var_1_0_1;
var_2_1_0 = var_0_1_0 + var_1_1_0;
var_2_1_1 = var_0_1_1 + var_1_1_1;
// step 3: Matrix transpose
AutoDiff<1,SIMD<double>> var_3_0_0;
AutoDiff<1,SIMD<double>> var_3_0_1;
AutoDiff<1,SIMD<double>> var_3_1_0;
AutoDiff<1,SIMD<double>> var_3_1_1;
var_3_0_0 = var_2_0_0;
var_3_0_1 = var_2_1_0;
var_3_1_0 = var_2_0_1;
var_3_1_1 = var_2_1_1;
// step 4: matrix-matrix multiply
AutoDiff<1,SIMD<double>> var_4_0_0;
AutoDiff<1,SIMD<double>> var_4_0_1;
AutoDiff<1,SIMD<double>> var_4_1_0;
AutoDiff<1,SIMD<double>> var_4_1_1;
var_4_0_0 = (((var_3_0_0 * var_2_0_0)) + (var_3_0_1 * var_2_1_0));
var_4_0_1 = (((var_3_0_0 * var_2_0_1)) + (var_3_0_1 * var_2_1_1));
var_4_1_0 = (((var_3_1_0 * var_2_0_0)) + (var_3_1_1 * var_2_1_0));
var_4_1_1 = (((var_3_1_0 * var_2_0_1)) + (var_3_1_1 * var_2_1_1));
// step 5: Identity matrix
AutoDiff<1,SIMD<double>> var_5_0_0;
AutoDiff<1,SIMD<double>> var_5_0_1;
AutoDiff<1,SIMD<double>> var_5_1_0;
AutoDiff<1,SIMD<double>> var_5_1_1;
var_5_0_0 = 1.0;
var_5_0_1 = 0.0;
var_5_1_0 = 0.0;
var_5_1_1 = 1.0;
// step 6: binary operation '-'
AutoDiff<1,SIMD<double>> var_6_0_0;
AutoDiff<1,SIMD<double>> var_6_0_1;
AutoDiff<1,SIMD<double>> var_6_1_0;
AutoDiff<1,SIMD<double>> var_6_1_1;
var_6_0_0 = var_4_0_0 - var_5_0_0;
var_6_0_1 = var_4_0_1 - var_5_0_1;
var_6_1_0 = var_4_1_0 - var_5_1_0;
var_6_1_1 = var_4_1_1 - var_5_1_1;
// step 7: trace
AutoDiff<1,SIMD<double>> var_7;
var_7 = ((var_6_0_0) + var_6_1_1);
// step 8: Determinant
Mat<2,2,AutoDiff<1,SIMD<double>>> mat_8;
mat_8(0,0) = var_2_0_0;
mat_8(0,1) = var_2_0_1;
mat_8(1,0) = var_2_1_0;
mat_8(1,1) = var_2_1_1;
AutoDiff<1,SIMD<double>> var_8;
var_8 = Det(mat_8);
// step 9: binary operation '*'
AutoDiff<1,SIMD<double>> var_9;
var_9 = var_8 * var_8;
// step 10: -0.333333
AutoDiff<1,SIMD<double>> var_10;
var_10 = -0x1.5555555555556p-2 /* (-3.3333333333333337e-01) */;
// step 11: binary operation 'pow'
AutoDiff<1,SIMD<double>> var_11;
var_11 = pow(var_9,var_10);
// step 12: scale 3
AutoDiff<1,SIMD<double>> var_12;
var_12 = (0x1.8p+1 /* (3.0000000000000000e+00) */ * var_11);
// step 13: binary operation '+'
AutoDiff<1,SIMD<double>> var_13;
var_13 = var_7 + var_12;
// step 14: 1
AutoDiff<1,SIMD<double>> var_14;
var_14 = 0x1p+0 /* (1.0000000000000000e+00) */;
// step 15: binary operation '-'
AutoDiff<1,SIMD<double>> var_15;
var_15 = var_13 - var_14;
// step 16: scale 43.75
AutoDiff<1,SIMD<double>> var_16;
var_16 = (0x1.5ep+5 /* (4.3750000000000000e+01) */ * var_15);
AutoDiff<1,SIMD<double>> var_17;
var_17 = var_16;
results(0,i) =var_17;
}
}
void CompiledEvaluateDDeriv(BaseMappedIntegrationRule & mir, BareSliceMatrix<AutoDiffDiff<1,double>> results ) {
FlatMatrix<double> values_1;
ProxyUserData * tmp_1_0 = (ProxyUserData*)mir.GetTransformation().userdata;
{
if (tmp_1_0->fel) {
auto x = tmp_1_0->GetMemory (reinterpret_cast<ProxyFunction*>(compiled_code_pointer52));
values_1.AssignMemory(x.Height(), x.Width(), &x(0,0));
}
}
[[maybe_unused]] const bool has_values_1 = tmp_1_0->HasMemory(reinterpret_cast<ProxyFunction*>(compiled_code_pointer52));
AutoDiffDiff<1,double> comp_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(( (tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer52)) && (tmp_1_0->trial_comp==0))
|| ((tmp_1_0->testfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer52)) && (tmp_1_0->test_comp==0)))
comp_1_0_0.DValue(0) = 1.0;
AutoDiffDiff<1,double> comp_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(( (tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer52)) && (tmp_1_0->trial_comp==1))
|| ((tmp_1_0->testfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer52)) && (tmp_1_0->test_comp==1)))
comp_1_0_1.DValue(0) = 1.0;
AutoDiffDiff<1,double> comp_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(( (tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer52)) && (tmp_1_0->trial_comp==2))
|| ((tmp_1_0->testfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer52)) && (tmp_1_0->test_comp==2)))
comp_1_1_0.DValue(0) = 1.0;
AutoDiffDiff<1,double> comp_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(( (tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer52)) && (tmp_1_0->trial_comp==3))
|| ((tmp_1_0->testfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer52)) && (tmp_1_0->test_comp==3)))
comp_1_1_1.DValue(0) = 1.0;
[[maybe_unused]] auto points = mir.GetPoints();
[[maybe_unused]] auto domain_index = mir.GetTransformation().GetElementIndex();
for ( auto i : Range(mir)) {
[[maybe_unused]] auto & ip = mir[i];
// step 0: Identity matrix
AutoDiffDiff<1,double> var_0_0_0;
AutoDiffDiff<1,double> var_0_0_1;
AutoDiffDiff<1,double> var_0_1_0;
AutoDiffDiff<1,double> var_0_1_1;
var_0_0_0 = 1.0;
var_0_0_1 = 0.0;
var_0_1_0 = 0.0;
var_0_1_1 = 1.0;
// step 1: trial-function diffop = grad
AutoDiffDiff<1,double> var_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_0 = 0.0;
AutoDiffDiff<1,double> var_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_1 = 0.0;
AutoDiffDiff<1,double> var_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_0 = 0.0;
AutoDiffDiff<1,double> var_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_1 = 0.0;
// if (tmp_1_0->fel) {
if (has_values_1) {
var_1_0_0.Value() = values_1(i,0);
var_1_0_1.Value() = values_1(i,1);
var_1_1_0.Value() = values_1(i,2);
var_1_1_1.Value() = values_1(i,3);
}
{
var_1_0_0.DValue(0) = comp_1_0_0.DValue(0);
var_1_0_1.DValue(0) = comp_1_0_1.DValue(0);
var_1_1_0.DValue(0) = comp_1_1_0.DValue(0);
var_1_1_1.DValue(0) = comp_1_1_1.DValue(0);
}
// step 2: binary operation '+'
AutoDiffDiff<1,double> var_2_0_0;
AutoDiffDiff<1,double> var_2_0_1;
AutoDiffDiff<1,double> var_2_1_0;
AutoDiffDiff<1,double> var_2_1_1;
var_2_0_0 = var_0_0_0 + var_1_0_0;
var_2_0_1 = var_0_0_1 + var_1_0_1;
var_2_1_0 = var_0_1_0 + var_1_1_0;
var_2_1_1 = var_0_1_1 + var_1_1_1;
// step 3: Matrix transpose
AutoDiffDiff<1,double> var_3_0_0;
AutoDiffDiff<1,double> var_3_0_1;
AutoDiffDiff<1,double> var_3_1_0;
AutoDiffDiff<1,double> var_3_1_1;
var_3_0_0 = var_2_0_0;
var_3_0_1 = var_2_1_0;
var_3_1_0 = var_2_0_1;
var_3_1_1 = var_2_1_1;
// step 4: matrix-matrix multiply
AutoDiffDiff<1,double> var_4_0_0;
AutoDiffDiff<1,double> var_4_0_1;
AutoDiffDiff<1,double> var_4_1_0;
AutoDiffDiff<1,double> var_4_1_1;
var_4_0_0 = (((var_3_0_0 * var_2_0_0)) + (var_3_0_1 * var_2_1_0));
var_4_0_1 = (((var_3_0_0 * var_2_0_1)) + (var_3_0_1 * var_2_1_1));
var_4_1_0 = (((var_3_1_0 * var_2_0_0)) + (var_3_1_1 * var_2_1_0));
var_4_1_1 = (((var_3_1_0 * var_2_0_1)) + (var_3_1_1 * var_2_1_1));
// step 5: Identity matrix
AutoDiffDiff<1,double> var_5_0_0;
AutoDiffDiff<1,double> var_5_0_1;
AutoDiffDiff<1,double> var_5_1_0;
AutoDiffDiff<1,double> var_5_1_1;
var_5_0_0 = 1.0;
var_5_0_1 = 0.0;
var_5_1_0 = 0.0;
var_5_1_1 = 1.0;
// step 6: binary operation '-'
AutoDiffDiff<1,double> var_6_0_0;
AutoDiffDiff<1,double> var_6_0_1;
AutoDiffDiff<1,double> var_6_1_0;
AutoDiffDiff<1,double> var_6_1_1;
var_6_0_0 = var_4_0_0 - var_5_0_0;
var_6_0_1 = var_4_0_1 - var_5_0_1;
var_6_1_0 = var_4_1_0 - var_5_1_0;
var_6_1_1 = var_4_1_1 - var_5_1_1;
// step 7: trace
AutoDiffDiff<1,double> var_7;
var_7 = ((var_6_0_0) + var_6_1_1);
// step 8: Determinant
Mat<2,2,AutoDiffDiff<1,double>> mat_8;
mat_8(0,0) = var_2_0_0;
mat_8(0,1) = var_2_0_1;
mat_8(1,0) = var_2_1_0;
mat_8(1,1) = var_2_1_1;
AutoDiffDiff<1,double> var_8;
var_8 = Det(mat_8);
// step 9: binary operation '*'
AutoDiffDiff<1,double> var_9;
var_9 = var_8 * var_8;
// step 10: -0.333333
AutoDiffDiff<1,double> var_10;
var_10 = -0x1.5555555555556p-2 /* (-3.3333333333333337e-01) */;
// step 11: binary operation 'pow'
AutoDiffDiff<1,double> var_11;
var_11 = pow(var_9,var_10);
// step 12: scale 3
AutoDiffDiff<1,double> var_12;
var_12 = (0x1.8p+1 /* (3.0000000000000000e+00) */ * var_11);
// step 13: binary operation '+'
AutoDiffDiff<1,double> var_13;
var_13 = var_7 + var_12;
// step 14: 1
AutoDiffDiff<1,double> var_14;
var_14 = 0x1p+0 /* (1.0000000000000000e+00) */;
// step 15: binary operation '-'
AutoDiffDiff<1,double> var_15;
var_15 = var_13 - var_14;
// step 16: scale 43.75
AutoDiffDiff<1,double> var_16;
var_16 = (0x1.5ep+5 /* (4.3750000000000000e+01) */ * var_15);
AutoDiffDiff<1,double> var_17;
var_17 = var_16;
results(i,0) =var_17;
}
}
void CompiledEvaluateDDerivSIMD(SIMD_BaseMappedIntegrationRule & mir, BareSliceMatrix<AutoDiffDiff<1,SIMD<double>>> results ) {
FlatMatrix<SIMD<double>> values_1;
ProxyUserData * tmp_1_0 = (ProxyUserData*)mir.GetTransformation().userdata;
{
if (tmp_1_0->fel) {
auto x = tmp_1_0->GetAMemory (reinterpret_cast<ProxyFunction*>(compiled_code_pointer53));
values_1.AssignMemory(x.Height(), x.Width(), &x(0,0));
}
}
[[maybe_unused]] const bool has_values_1 = tmp_1_0->HasMemory(reinterpret_cast<ProxyFunction*>(compiled_code_pointer53));
AutoDiffDiff<1,SIMD<double>> comp_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(( (tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer53)) && (tmp_1_0->trial_comp==0))
|| ((tmp_1_0->testfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer53)) && (tmp_1_0->test_comp==0)))
comp_1_0_0.DValue(0) = 1.0;
AutoDiffDiff<1,SIMD<double>> comp_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(( (tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer53)) && (tmp_1_0->trial_comp==1))
|| ((tmp_1_0->testfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer53)) && (tmp_1_0->test_comp==1)))
comp_1_0_1.DValue(0) = 1.0;
AutoDiffDiff<1,SIMD<double>> comp_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
if(( (tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer53)) && (tmp_1_0->trial_comp==2))
|| ((tmp_1_0->testfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer53)) && (tmp_1_0->test_comp==2)))
comp_1_1_0.DValue(0) = 1.0;
AutoDiffDiff<1,SIMD<double>> comp_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
if(( (tmp_1_0->trialfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer53)) && (tmp_1_0->trial_comp==3))
|| ((tmp_1_0->testfunction == reinterpret_cast<ProxyFunction*>(compiled_code_pointer53)) && (tmp_1_0->test_comp==3)))
comp_1_1_1.DValue(0) = 1.0;
[[maybe_unused]] auto points = mir.GetPoints();
[[maybe_unused]] auto domain_index = mir.GetTransformation().GetElementIndex();
for ( auto i : Range(mir)) {
[[maybe_unused]] auto & ip = mir[i];
// step 0: Identity matrix
AutoDiffDiff<1,SIMD<double>> var_0_0_0;
AutoDiffDiff<1,SIMD<double>> var_0_0_1;
AutoDiffDiff<1,SIMD<double>> var_0_1_0;
AutoDiffDiff<1,SIMD<double>> var_0_1_1;
var_0_0_0 = 1.0;
var_0_0_1 = 0.0;
var_0_1_0 = 0.0;
var_0_1_1 = 1.0;
// step 1: trial-function diffop = grad
AutoDiffDiff<1,SIMD<double>> var_1_0_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_0 = 0.0;
AutoDiffDiff<1,SIMD<double>> var_1_0_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_0_1 = 0.0;
AutoDiffDiff<1,SIMD<double>> var_1_1_0(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_0 = 0.0;
AutoDiffDiff<1,SIMD<double>> var_1_1_1(0x0p+0 /* (0.0000000000000000e+00) */);
var_1_1_1 = 0.0;
if (has_values_1) {
var_1_0_0.Value() = values_1(0,i);
var_1_0_1.Value() = values_1(1,i);
var_1_1_0.Value() = values_1(2,i);
var_1_1_1.Value() = values_1(3,i);
}
{
var_1_0_0.DValue(0) = comp_1_0_0.DValue(0);
var_1_0_1.DValue(0) = comp_1_0_1.DValue(0);
var_1_1_0.DValue(0) = comp_1_1_0.DValue(0);
var_1_1_1.DValue(0) = comp_1_1_1.DValue(0);
}
// step 2: binary operation '+'
AutoDiffDiff<1,SIMD<double>> var_2_0_0;
AutoDiffDiff<1,SIMD<double>> var_2_0_1;
AutoDiffDiff<1,SIMD<double>> var_2_1_0;
AutoDiffDiff<1,SIMD<double>> var_2_1_1;
var_2_0_0 = var_0_0_0 + var_1_0_0;
var_2_0_1 = var_0_0_1 + var_1_0_1;
var_2_1_0 = var_0_1_0 + var_1_1_0;
var_2_1_1 = var_0_1_1 + var_1_1_1;
// step 3: Matrix transpose
AutoDiffDiff<1,SIMD<double>> var_3_0_0;
AutoDiffDiff<1,SIMD<double>> var_3_0_1;
AutoDiffDiff<1,SIMD<double>> var_3_1_0;
AutoDiffDiff<1,SIMD<double>> var_3_1_1;
var_3_0_0 = var_2_0_0;
var_3_0_1 = var_2_1_0;
var_3_1_0 = var_2_0_1;
var_3_1_1 = var_2_1_1;
// step 4: matrix-matrix multiply
AutoDiffDiff<1,SIMD<double>> var_4_0_0;
AutoDiffDiff<1,SIMD<double>> var_4_0_1;
AutoDiffDiff<1,SIMD<double>> var_4_1_0;
AutoDiffDiff<1,SIMD<double>> var_4_1_1;
var_4_0_0 = (((var_3_0_0 * var_2_0_0)) + (var_3_0_1 * var_2_1_0));
var_4_0_1 = (((var_3_0_0 * var_2_0_1)) + (var_3_0_1 * var_2_1_1));
var_4_1_0 = (((var_3_1_0 * var_2_0_0)) + (var_3_1_1 * var_2_1_0));
var_4_1_1 = (((var_3_1_0 * var_2_0_1)) + (var_3_1_1 * var_2_1_1));
// step 5: Identity matrix
AutoDiffDiff<1,SIMD<double>> var_5_0_0;
AutoDiffDiff<1,SIMD<double>> var_5_0_1;
AutoDiffDiff<1,SIMD<double>> var_5_1_0;
AutoDiffDiff<1,SIMD<double>> var_5_1_1;
var_5_0_0 = 1.0;
var_5_0_1 = 0.0;
var_5_1_0 = 0.0;
var_5_1_1 = 1.0;
// step 6: binary operation '-'
AutoDiffDiff<1,SIMD<double>> var_6_0_0;
AutoDiffDiff<1,SIMD<double>> var_6_0_1;
AutoDiffDiff<1,SIMD<double>> var_6_1_0;
AutoDiffDiff<1,SIMD<double>> var_6_1_1;
var_6_0_0 = var_4_0_0 - var_5_0_0;
var_6_0_1 = var_4_0_1 - var_5_0_1;
var_6_1_0 = var_4_1_0 - var_5_1_0;
var_6_1_1 = var_4_1_1 - var_5_1_1;
// step 7: trace
AutoDiffDiff<1,SIMD<double>> var_7;
var_7 = ((var_6_0_0) + var_6_1_1);
// step 8: Determinant
Mat<2,2,AutoDiffDiff<1,SIMD<double>>> mat_8;
mat_8(0,0) = var_2_0_0;
mat_8(0,1) = var_2_0_1;
mat_8(1,0) = var_2_1_0;
mat_8(1,1) = var_2_1_1;
AutoDiffDiff<1,SIMD<double>> var_8;
var_8 = Det(mat_8);
// step 9: binary operation '*'
AutoDiffDiff<1,SIMD<double>> var_9;
var_9 = var_8 * var_8;
// step 10: -0.333333
AutoDiffDiff<1,SIMD<double>> var_10;
var_10 = -0x1.5555555555556p-2 /* (-3.3333333333333337e-01) */;
// step 11: binary operation 'pow'
AutoDiffDiff<1,SIMD<double>> var_11;
var_11 = pow(var_9,var_10);
// step 12: scale 3
AutoDiffDiff<1,SIMD<double>> var_12;
var_12 = (0x1.8p+1 /* (3.0000000000000000e+00) */ * var_11);
// step 13: binary operation '+'
AutoDiffDiff<1,SIMD<double>> var_13;
var_13 = var_7 + var_12;
// step 14: 1
AutoDiffDiff<1,SIMD<double>> var_14;
var_14 = 0x1p+0 /* (1.0000000000000000e+00) */;
// step 15: binary operation '-'
AutoDiffDiff<1,SIMD<double>> var_15;
var_15 = var_13 - var_14;
// step 16: scale 43.75
AutoDiffDiff<1,SIMD<double>> var_16;
var_16 = (0x1.5ep+5 /* (4.3750000000000000e+01) */ * var_15);
AutoDiffDiff<1,SIMD<double>> var_17;
var_17 = var_16;
results(0,i) =var_17;
}
}
}