| /libCEED/examples/solids/ |
| H A D | index.md | 102 \bm{\Phi} = \frac{\lambda}{2} (\operatorname{trace} \bm{\epsilon})^2 + \mu \bm{\epsilon} : \bm{\eps…
108 \bm\sigma = \lambda (\operatorname{trace} \bm\epsilon) \bm I_3 + 2 \mu \bm\epsilon,
114 \begin{aligned} \lambda &= \frac{E \nu}{(1 + \nu)(1 - 2 \nu)} \\ \mu &= \frac{E}{2(1 + \nu)} \end{a…
128 \lambda + 2\mu & \lambda & \lambda & & & \\
129 \lambda & \lambda + 2\mu & \lambda & & & \\
130 \lambda & \lambda & \lambda + 2\mu & & & \\
137 Note that the incompressible limit $\nu \to \frac 1 2$ causes $\lambda \to \infty$, and thus $\math…
147 \bm{\Phi} = \lambda (1 + \operatorname{trace} \bm{\epsilon}) (\log(1 + \operatorname{trace} \bm\eps…
153 \bm{\sigma} = \lambda \log(1 + \operatorname{trace} \bm\epsilon) \bm{I}_3 + 2\mu \bm{\epsilon}
182 \diff \bm{\sigma} = \bar{\lambda} \cdot \operatorname{trace} \diff \bm{\epsilon} \cdot \bm{I}_3 + …
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| H A D | README.md | 237 - $\lambda \operatorname{trace} \bm{\epsilon}$
238 - $\lambda \log \operatorname{trace} \bm{\epsilon}$
239 - $\lambda \log J$
257 … - $\frac{\lambda}{2} (\operatorname{trace} \bm{\epsilon})^2 + \mu \bm{\epsilon} : \bm{\epsilon}$
258 …- $\lambda (1 + \operatorname{trace} \bm{\epsilon}) (\log(1 + \operatorname{trace} \bm{\epsilon} )…
259 - $\frac{\lambda}{2}(\log J)^2 + \mu \operatorname{trace} \bm{E} - \mu \log J$
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| /libCEED/examples/solids/qfunctions/ |
| H A D | finite-strain-mooney-rivlin.h | 26 CeedScalar lambda; member
102 …ommonFSMR(const CeedScalar mu_1, const CeedScalar mu_2, const CeedScalar lambda, const CeedScalar … in commonFSMR() argument
148 …Swork[i] = (lambda * *logJ - mu_1 - 2 * mu_2) * Cinvwork[i] + (mu_1 + mu_2 * I_1) * (i < 3) // id… in commonFSMR()
171 const CeedScalar lambda = context->lambda; in ElasFSResidual_MR() local
223 commonFSMR(mu_1, mu_2, lambda, tempgradu, Swork, Cwork, Cinvwork, &logJ); in ElasFSResidual_MR()
270 const CeedScalar lambda = context->lambda; in ElasFSJacobian_MR() local
316 commonFSMR(mu_1, mu_2, lambda, tempgradu, Swork, Cwork, Cinvwork, &logJ); in ElasFSJacobian_MR()
380 …dSwork[i] = lambda * Cinv_contract_dE * Cinvwork[i] + 2 * (mu_1 + 2 * mu_2 - lambda * logJ) * Cinv… in ElasFSJacobian_MR()
430 const CeedScalar lambda = context->lambda; in ElasFSEnergy_MR() local
500 …energy[i] = (0.5 * lambda * (logJ) * (logJ) - (mu_1 + 2 * mu_2) * logJ + (mu_1 / 2.) * (I_1 - 3) +… in ElasFSEnergy_MR()
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| H A D | finite-strain-neo-hookean.h | 98 CEED_QFUNCTION_HELPER int commonFS(const CeedScalar lambda, const CeedScalar mu, const CeedScalar g… in commonFS() argument
137 Swork[m] = (lambda * (*logJ)) * Cinvwork[m]; in commonFS()
163 const CeedScalar lambda = (3 * Kbulk - TwoMu) / 3; in ElasFSResidual_NH() local
220 commonFS(lambda, mu, tempgradu, Swork, Cinvwork, &logJ); in ElasFSResidual_NH()
272 const CeedScalar lambda = (3 * Kbulk - TwoMu) / 3; in ElasFSJacobian_NH() local
316 commonFS(lambda, mu, tempgradu, Swork, Cinvwork, &logJ); in ElasFSJacobian_NH()
371 …for (CeedInt k = 0; k < 3; k++) deltaS[j][k] = lambda * Cinv_contract_E * C_inv[j][k] - 2. * (lamb… in ElasFSJacobian_NH()
412 const CeedScalar lambda = (3 * Kbulk - TwoMu) / 3; in ElasFSEnergy_NH() local
458 …energy[i] = (lambda * logJ * logJ / 2. - mu * logJ + mu * (E2[0][0] + E2[1][1] + E2[2][2]) / 2.) *… in ElasFSEnergy_NH()
483 const CeedScalar lambda = (3 * Kbulk - TwoMu) / 3; in ElasFSDiagnostic_NH() local
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| H A D | linear.h | 235 const CeedScalar lambda = (3 * Kbulk - TwoMu) / 3; in ElasEnergy_Linear() local
276 …(lambda * strain_vol * strain_vol / 2. + strain_vol * mu + (e[0][1] * e[0][1] + e[0][2] * e[0][2] … in ElasEnergy_Linear()
303 const CeedScalar lambda = (3 * Kbulk - TwoMu) / 3; in ElasDiagnostic_Linear() local
347 diagnostic[3][i] = -lambda * strain_vol; in ElasDiagnostic_Linear()
359 …(lambda * strain_vol * strain_vol / 2. + strain_vol * mu + (e[0][1] * e[0][1] + e[0][2] * e[0][2] … in ElasDiagnostic_Linear()
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| /libCEED/tests/ |
| H A D | t304-basis.c | 14 CeedScalar M[16], Q[16], lambda[4], Q_lambda_Qt[16]; in main() local
33 CeedSymmetricSchurDecomposition(ceed, Q, lambda, p); in main()
39 for (int k = 0; k < p; k++) sum += Q[p * i + k] * lambda[k] * Q[p * j + k]; in main()
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| H A D | t305-basis.c | 14 CeedScalar M[p * p], K[p * p], X[p * p], lambda[p]; in main() local
37 CeedSimultaneousDiagonalization(ceed, K, M, X, lambda, p); in main()
82 if (fabs(K[p * i + j] - (i == j ? lambda[i] : 0.0)) > 1e3 * CEED_EPSILON) { in main()
84 …[%" CeedInt_FMT ", %" CeedInt_FMT "]: %f != %f\n", i, j, K[p * i + j], (i == j ? lambda[i] : 0.0)); in main()
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| /libCEED/examples/solids/problems/ |
| H A D | mooney-rivlin.c | 54 …phys_smoother->lambda = 2 * (phys_smoother->mu_1 + phys_smoother->mu_2) * nu_smoother / (1 - 2 * n… in PhysicsSmootherContext_MR()
69 phys->lambda = -1; in ProcessPhysics_MR()
86 phys->lambda = 2 * (phys->mu_1 + phys->mu_2) * nu / (1 - 2 * nu); in ProcessPhysics_MR()
105 phys->lambda *= units->Pascal; in ProcessPhysics_MR()
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| H A D | mooney-rivlin.h | 21 CeedScalar lambda; member
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| /libCEED/examples/petsc/qfunctions/bps/ |
| H A D | bp4sphere.h | 40 const CeedScalar lambda = atan2(y, x); // longitude in SetupDiffRhs3() local
44 true_soln[i + 0 * Q] = sin(lambda) * cos(theta); in SetupDiffRhs3()
51 rhs[i + 0 * Q] = q_data[i + Q * 0] * 2 * sin(lambda) * cos(theta) / (R * R); in SetupDiffRhs3()
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| H A D | bp3sphere.h | 163 const CeedScalar lambda = atan2(y, x); // longitude in SetupDiffRhs() local
165 true_soln[i + Q * 0] = sin(lambda) * cos(theta); in SetupDiffRhs()
167 rhs[i + Q * 0] = q_data[i + Q * 0] * 2 * sin(lambda) * cos(theta) / (R * R); in SetupDiffRhs()
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| /libCEED/examples/petsc/src/ |
| H A D | petscutils.c | 87 PetscScalar lambda = (x - layer / 6.0) * 6; in Kershaw() local
97 c[i + 1] = step(left(eps, y), right(eps, y), lambda); in Kershaw()
98 c[i + 2] = step(left(eps, z), right(eps, z), lambda); in Kershaw()
101 c[i + 1] = step(right(eps, y), left(eps, y), lambda / 2); in Kershaw()
102 c[i + 2] = step(right(eps, z), left(eps, z), lambda / 2); in Kershaw()
105 c[i + 1] = step(right(eps, y), left(eps, y), (1 + lambda) / 2); in Kershaw()
106 c[i + 2] = step(right(eps, z), left(eps, z), (1 + lambda) / 2); in Kershaw()
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| /libCEED/examples/fluids/qfunctions/ |
| H A D | newtonian_types.h | 24 CeedScalar lambda; member
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| H A D | newtonian_state.h | 559 stress[i] = gas->mu * (2 * strain_rate[i] + gas->lambda * div_u * (i < 3)); in NewtonianStress()
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| /libCEED/examples/fluids/problems/ |
| H A D | newtonian.c | 245 CeedScalar lambda = -2. / 3.; // - in NS_NEWTONIAN_IG() local
325 …sScalar("-lambda", "Stokes hypothesis second viscosity coefficient", NULL, lambda, &lambda, NULL)); in NS_NEWTONIAN_IG()
414 newtonian_ig_ctx->lambda = lambda; in NS_NEWTONIAN_IG()
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| /libCEED/interface/ |
| H A D | ceed-basis.c | 1300 int CeedSymmetricSchurDecomposition(Ceed ceed, CeedScalar *mat, CeedScalar *lambda, CeedInt n) { in CeedSymmetricSchurDecomposition() argument
1420 for (CeedInt i = 0; i < n; i++) lambda[i] = mat_T[i + n * i]; in CeedSymmetricSchurDecomposition()
1447 …eed ceed, CeedScalar *mat_A, CeedScalar *mat_B, CeedScalar *mat_X, CeedScalar *lambda, CeedInt n) { in CeedSimultaneousDiagonalization() argument
1486 CeedCall(CeedSymmetricSchurDecomposition(ceed, mat_C, lambda, n)); in CeedSimultaneousDiagonalization()
1491 if (fabs(lambda[j]) > fabs(lambda[j + 1])) { in CeedSimultaneousDiagonalization()
1492 CeedScalarSwap(lambda[j], lambda[j + 1]); in CeedSimultaneousDiagonalization()
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| H A D | ceed-preconditioning.c | 2908 CeedScalar *mass, *laplace, *x, *fdm_interp, *lambda, *elem_avg; in CeedOperatorCreateFDMElementInverse() local
2975 CeedCall(CeedCalloc(P_1d, &lambda)); in CeedOperatorCreateFDMElementInverse()
2983 CeedCall(CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P_1d)); in CeedOperatorCreateFDMElementInverse()
3047 fdm_diagonal[c * num_nodes + n] += lambda[i]; in CeedOperatorCreateFDMElementInverse()
3081 CeedCall(CeedFree(&lambda)); in CeedOperatorCreateFDMElementInverse()
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| /libCEED/include/ceed/ |
| H A D | backend.h | 486 CEED_EXTERN int CeedSymmetricSchurDecomposition(Ceed ceed, CeedScalar *mat, CeedScalar *lambda, Cee…
487 …ion(Ceed ceed, CeedScalar *mat_A, CeedScalar *mat_B, CeedScalar *x, CeedScalar *lambda, CeedInt n);
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| /libCEED/julia/LibCEED.jl/src/generated/ |
| H A D | libceed_bindings.jl | 1466 function CeedSymmetricSchurDecomposition(ceed, mat, lambda, n) argument
1467 …mposition, libceed), Cint, (Ceed, Ptr{CeedScalar}, Ptr{CeedScalar}, CeedInt), ceed, mat, lambda, n)
1470 function CeedSimultaneousDiagonalization(ceed, mat_A, mat_B, x, lambda, n) argument
1471 …ar}, Ptr{CeedScalar}, Ptr{CeedScalar}, Ptr{CeedScalar}, CeedInt), ceed, mat_A, mat_B, x, lambda, n)
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| /libCEED/examples/fluids/ |
| H A D | README.md | 592 * - `-lambda`
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| H A D | index.md | 27 …)^T + \lambda (\nabla \cdot \bm{u})\bm{I}_3)$ is the Cauchy (symmetric) stress tensor, with $\mu$ …
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