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/libCEED/examples/fluids/
H A DSTGInflow_blasius.dat2 …e+00 0.000000000000000000e+00 0.000000000000000000e+00 0.000000000000000000e+00 1.0000000000000000…
3 …e-06 6.641140981505948560e-01 3.630359440264661799e-05 0.000000000000000000e+00 1.0000000000000000…
4 …e-06 6.827985921104507971e-01 3.837509590908312938e-05 0.000000000000000000e+00 1.0000000000000000…
5 …e-06 7.020087597129041068e-01 4.056479791879753598e-05 0.000000000000000000e+00 1.0000000000000000…
6 …e-06 7.217593898384206952e-01 4.287944492540062035e-05 0.000000000000000000e+00 1.0000000000000000…
7 …e-06 7.420656873629547512e-01 4.532616625247044189e-05 0.000000000000000000e+00 1.0000000000000000…
8 …e-06 7.629432848520516508e-01 4.791249800990936422e-05 0.000000000000000000e+00 1.0000000000000000…
9 …e-06 7.844082545828384712e-01 5.064640630279787997e-05 0.000000000000000000e+00 1.0000000000000000…
10 …e-06 8.064771209029573118e-01 5.353631176415636492e-05 0.000000000000000000e+00 1.0000000000000000…
11 …e-06 8.291668729357855039e-01 5.659111548710616638e-05 0.000000000000000000e+00 1.0000000000000000…
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H A Dnavierstokes.c1 // Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
4 // SPDX-License-Identifier: BSD-2-Clause
8 // libCEED + PETSc Example: Navier-Stokes
10 // This example demonstrates a simple usage of libCEED with PETSc to solve a Navier-Stokes problem.
18 // ./navierstokes -ceed /cpu/self -options_file gaussianwave.yml
19 // ./navierstokes -ceed /gpu/cuda -problem advection -degree 1
21 …-ceed {ceed_resource} -test_type solver -options_file examples/fluids/gaussianwave.yaml -compare_f…
22 …-ceed {ceed_resource} -test_type solver -options_file examples/fluids/gaussianwave.yaml -compare_f…
23 …-ceed {ceed_resource} -test_type solver -options_file examples/fluids/gaussianwave.yaml -compare_f…
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H A Dadvection.yaml13 units_kilogram: 1e-9
16 atol: 1e-4
17 rtol: 1e-3
21 atol: 1e-3
28 dt: 1e-3
/libCEED/examples/fluids/tests-output/
H A Ddiff_filter_mms_y_spacing.dat2 0.00000000e-00
3 1.02996826e-03
4 2.12542713e-03
5 3.28713586e-03
6 4.52012056e-03
7 5.83032053e-03
8 7.22210482e-03
9 8.69917590e-03
10 1.02688847e-02
11 1.19348252e-02
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/libCEED/examples/solids/tests-output/
H A DMR-strain1.csv2 0.000000,0.000000e+00
3 0.066667,5.210502e-03
4 0.133333,2.079358e-02
5 0.200000,4.636534e-02
6 0.266667,8.073178e-02
7 0.333333,1.217654e-01
8 0.400000,1.670271e-01
9 0.466667,2.146438e-01
10 0.533333,2.636486e-01
11 0.600000,3.138221e-01
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H A DMR-strain.csv2 0.000000,0.000000e+00
3 0.066667,5.271562e-03
4 0.133333,2.069557e-02
5 0.200000,4.509268e-02
6 0.266667,7.661738e-02
7 0.333333,1.131503e-01
8 0.400000,1.528054e-01
9 0.466667,1.942671e-01
10 0.533333,2.368184e-01
11 0.600000,2.801812e-01
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H A DNH-strain.csv2 0.000000,0.000000e+00
3 0.066667,5.271562e-03
4 0.133333,2.069557e-02
5 0.200000,4.509268e-02
6 0.266667,7.661738e-02
7 0.333333,1.131503e-01
8 0.400000,1.528054e-01
9 0.466667,1.942671e-01
10 0.533333,2.368184e-01
11 0.600000,2.801812e-01
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/libCEED/backends/memcheck/
H A Dceed-memcheck-restriction.c1 // Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
4 // SPDX-License-Identifier: BSD-2-Clause
14 #include "ceed-memcheck.h"
16 //------------------------------------------------------------------------------
18 //------------------------------------------------------------------------------
43 //------------------------------------------------------------------------------
45 //------------------------------------------------------------------------------
59 for (CeedSize e = start * block_size; e < stop * block_size; e += block_size) { in CeedElemRestrictionApplyStridedNoTranspose_Memcheck_Core() local
63 vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] = in CeedElemRestrictionApplyStridedNoTranspose_Memcheck_Core()
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/libCEED/backends/ref/
H A Dceed-ref-restriction.c1 // Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
4 // SPDX-License-Identifier: BSD-2-Clause
14 #include "ceed-ref.h"
16 //------------------------------------------------------------------------------
18 //------------------------------------------------------------------------------
30 for (CeedSize e = start * block_size; e < stop * block_size; e += block_size) { in CeedElemRestrictionApplyStridedNoTranspose_Ref_Core() local
34 vv[e * elem_size * num_comp + (k * elem_size + n) * block_size + j - v_offset] = in CeedElemRestrictionApplyStridedNoTranspose_Ref_Core()
35 … uu[n + k * elem_size + CeedIntMin(e + j, num_elem - 1) * elem_size * (CeedSize)num_comp]; in CeedElemRestrictionApplyStridedNoTranspose_Ref_Core()
45 for (CeedSize e = start * block_size; e < stop * block_size; e += block_size) { in CeedElemRestrictionApplyStridedNoTranspose_Ref_Core() local
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/libCEED/examples/solids/qfunctions/
H A Dlinear.h1 // Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
4 // SPDX-License-Identifier: BSD-2-Clause
21 CeedScalar E; // Young's Modulus member
25 // -----------------------------------------------------------------------------
27 // -----------------------------------------------------------------------------
39 const CeedScalar E = context->E; in ElasResidual_Linear() local
40 const CeedScalar nu = context->nu; in ElasResidual_Linear()
50 // -- Qdata in ElasResidual_Linear()
59 // dXdx = (dx/dX)^(-1) in ElasResidual_Linear()
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H A Dmanufactured-force.h1 // Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
4 // SPDX-License-Identifier: BSD-2-Clause
21 CeedScalar E; // Young's Modulus member
25 // -----------------------------------------------------------------------------
27 // -----------------------------------------------------------------------------
37 const CeedScalar E = context->E; in SetupMMSForce() local
38 const CeedScalar nu = context->nu; in SetupMMSForce()
47 // -- Component 1 in SetupMMSForce()
48 …orce[i + 0 * Q] = (-(E * (cos(x * 2.0) * cos(y * 3.0) * exp(z * 4.0) * 4.0 - cos(z * 4.0) * sin(y … in SetupMMSForce()
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/libCEED/benchmarks/
H A Dpostprocess_plot.py3 # Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors.
4 # All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
6 # SPDX-License-Identifier: BSD-2-Clause
16 log_y = 0 # use log scale on the y-axis?
17 x_range = (1e1, 4e6) # plot range for the x-axis; comment out for auto
18 y_range = (0, 2e9) # plot range for the y-axis; comment out for auto
33 rcParams['font.sans-serif'].insert(0, 'Noto Sans')
34 rcParams['font.sans-serif'].insert(1, 'Open Sans')
51 test_short = test.strip().split()[0] + ' BP' + test.strip().split()[-1]
107 d = [[e[2], e[3]] for e in d if e[0] == sol_p]
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/libCEED/include/ceed/jit-source/hip/
H A Dhip-ref-operator-assemble.h1 // Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
4 // SPDX-License-Identifier: BSD-2-Clause
18 //------------------------------------------------------------------------------
20 //------------------------------------------------------------------------------
31 …mined by the reference (interface) implementation of the symbolic assembly, slowest --> fastest: e, in __launch_bounds__()
37 // Strides for QF array, slowest --> fastest: e_in, comp_in, e_out, comp_out, e, q in __launch_bounds__()
45 …for (IndexType e = blockIdx.x * blockDim.z + threadIdx.z; e < num_elem; e += gridDim.x * blockDim.… in __launch_bounds__() local
50 …exType qf_index_comp = q_comp_in_stride * comp_in + q_comp_out_stride * comp_out + q_e_stride * e; in __launch_bounds__()
66 result *= orients_in[NUM_NODES_IN * e + l] ? -1.0 : 1.0; in __launch_bounds__()
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/libCEED/include/ceed/jit-source/cuda/
H A Dcuda-ref-operator-assemble.h1 // Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
4 // SPDX-License-Identifier: BSD-2-Clause
18 //------------------------------------------------------------------------------
20 //------------------------------------------------------------------------------
31 …mined by the reference (interface) implementation of the symbolic assembly, slowest --> fastest: e, in __launch_bounds__()
37 // Strides for QF array, slowest --> fastest: e_in, comp_in, e_out, comp_out, e, q in __launch_bounds__()
45 …for (IndexType e = blockIdx.x * blockDim.z + threadIdx.z; e < num_elem; e += gridDim.x * blockDim.… in __launch_bounds__() local
50 …exType qf_index_comp = q_comp_in_stride * comp_in + q_comp_out_stride * comp_out + q_e_stride * e; in __launch_bounds__()
66 result *= orients_in[NUM_NODES_IN * e + l] ? -1.0 : 1.0; in __launch_bounds__()
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/libCEED/examples/solids/
H A Dindex.md1 (example-petsc-elasticity)=
3 # Solid mechanics mini-app
6 It solves the steady-state static momentum balance equations using unstructured high-order finite/s…
7 As for the {ref}`example-petsc-navier-stokes` case, the solid mechanics elasticity example has been…
9 …ini-app, we consider three formulations used in solid mechanics applications: linear elasticity, N…
11 The stress-strain relationship (constitutive law) for each of the material models is provided.
12 Due to the nonlinearity of material models in Neo-Hookean hyperelasticity, the Newton linearization…
15 Linear elasticity and small-strain hyperelasticity can both by obtained from the finite-strain hype…
16 …ain regime, while $\bm S$ and $\bm E$ are their finite-strain generalizations (second Piola-Kircho…
20 {\overbrace{\bm S(\bm E)}^{\text{Finite Strain Hyperelastic}}}
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H A DREADME.md7 This code solves the steady-state static momentum balance equations using unstructured high-order f…
8 …ini-app, we consider three formulations used in solid mechanics applications: linear elasticity, N…
20 ./elasticity -mesh [.exo file] -degree [degree] -nu [nu] -E [E] [boundary options] -problem [proble…
25 <!-- solids-inclusion -->
27 The elasticity mini-app is controlled via command-line options, the following of which are mandator…
29 :::{list-table} Mandatory Runtime Options
30 :header-rows: 1
33 * - Option
34 - Description
35 * - `-mesh [filename]`
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/libCEED/tests/
H A Dt598-operator.c4 #include "t591-operator.h"
15 … num_nodes_coarse = (num_elem_1d * (p_coarse - 1) + 1) * (num_elem_1d * (p_coarse - 1)… in main()
16 …Int num_nodes_fine = (num_elem_1d * (p_fine - 1) + 1) * (num_elem_1d * (p_fine - 1) … in main()
30 for (CeedInt e = 0; e < num_elem; e++) { in main() local
32 x_array[num_points_per_elem * (e * dim + d) + 0] = 0.25; in main()
33 x_array[num_points_per_elem * (e * dim + d) + 1] = d == 0 ? -0.25 : 0.25; in main()
34 x_array[num_points_per_elem * (e * dim + d) + 2] = d == 0 ? 0.25 : -0.25; in main()
35 x_array[num_points_per_elem * (e * dim + d) + 3] = 0.25; in main()
55 CeedInt p = 2, num_nodes = (num_elem_1d * (p - 1) + 1) * (num_elem_1d * (p - 1) + 1); in main()
58 for (CeedInt e = 0; e < num_elem; e++) { in main() local
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H A Dt591-operator.c4 #include "t591-operator.h"
14 …CeedInt num_nodes = (num_elem_1d * (p - 1) + 1) * (num_elem_1d * (p - 1) + 1), num_points_per_elem… in main()
29 for (CeedInt e = 0; e < num_elem; e++) { in main() local
31 x_array[num_points_per_elem * (e * dim + d) + 0] = 0.25; in main()
32 x_array[num_points_per_elem * (e * dim + d) + 1] = d == 0 ? -0.25 : 0.25; in main()
33 x_array[num_points_per_elem * (e * dim + d) + 2] = d == 0 ? 0.25 : -0.25; in main()
34 x_array[num_points_per_elem * (e * dim + d) + 3] = 0.25; in main()
54 CeedInt p = 2, num_nodes = (num_elem_1d * (p - 1) + 1) * (num_elem_1d * (p - 1) + 1); in main()
57 for (CeedInt e = 0; e < num_elem; e++) { in main() local
60 for (CeedInt d = 0; d < dim; d++) n_d[d] = num_elem_1d * (p - 1) + 1; in main()
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H A Dt590-operator.c4 #include "t590-operator.h"
14 …CeedInt num_nodes = (num_elem_1d * (p - 1) + 1) * (num_elem_1d * (p - 1) + 1), num_points_per_elem… in main()
28 for (CeedInt e = 0; e < num_elem; e++) { in main() local
30 x_array[num_points_per_elem * (e * dim + d) + 0] = 0.25; in main()
31 x_array[num_points_per_elem * (e * dim + d) + 1] = d == 0 ? -0.25 : 0.25; in main()
32 x_array[num_points_per_elem * (e * dim + d) + 2] = d == 0 ? 0.25 : -0.25; in main()
33 x_array[num_points_per_elem * (e * dim + d) + 3] = 0.25; in main()
50 for (CeedInt e = 0; e < num_elem; e++) { in main() local
53 for (CeedInt d = 0; d < dim; d++) n_d[d] = num_elem_1d * (p - 1) + 1; in main()
55 CeedInt r_e = e; in main()
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H A Dt595-operator.c4 #include "t595-operator.h"
14 …CeedInt num_nodes = (num_elem_1d * (p - 1) + 1) * (num_elem_1d * (p - 1) + 1), num_points_per_elem… in main()
30 for (CeedInt e = 0; e < num_elem; e++) { in main() local
32 x_array[num_points_per_elem * (e * dim + d) + 0] = 0.25; in main()
33 x_array[num_points_per_elem * (e * dim + d) + 1] = d == 0 ? -0.25 : 0.25; in main()
34 x_array[num_points_per_elem * (e * dim + d) + 2] = d == 0 ? 0.25 : -0.25; in main()
35 x_array[num_points_per_elem * (e * dim + d) + 3] = 0.25; in main()
59 for (CeedInt e = 0; e < num_elem; e++) { in main() local
62 for (CeedInt d = 0; d < dim; d++) n_d[d] = num_elem_1d * (p - 1) + 1; in main()
64 CeedInt r_e = e; in main()
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H A Dt592-operator.c9 #include "t591-operator.h"
14 …CeedInt num_nodes = (num_elem_1d * (p - 1) + 1) * (num_elem_1d * (p - 1) + 1), num_points_per_elem… in main()
29 for (CeedInt e = 0; e < num_elem; e++) { in main() local
31 x_array[num_points_per_elem * (e * dim + d) + 0] = 0.25; in main()
32 x_array[num_points_per_elem * (e * dim + d) + 1] = d == 0 ? -0.25 : 0.25; in main()
33 x_array[num_points_per_elem * (e * dim + d) + 2] = d == 0 ? 0.25 : -0.25; in main()
34 x_array[num_points_per_elem * (e * dim + d) + 3] = 0.25; in main()
54 CeedInt p = 2, num_nodes = (num_elem_1d * (p - 1) + 1) * (num_elem_1d * (p - 1) + 1); in main()
57 for (CeedInt e = 0; e < num_elem; e++) { in main() local
60 for (CeedInt d = 0; d < dim; d++) n_d[d] = num_elem_1d * (p - 1) + 1; in main()
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H A Dt599-operator.c4 #include "t599-operator.h"
13 …CeedInt num_nodes = (num_elem_1d * (p - 1) + 1) * (num_elem_1d * (p - 1) + 1), num_points_per_elem… in main()
27 for (CeedInt e = 0; e < num_elem; e++) { in main() local
29 x_array[num_points_per_elem * (e * dim + d) + 0] = 0.25; in main()
30 x_array[num_points_per_elem * (e * dim + d) + 1] = d == 0 ? -0.25 : 0.25; in main()
31 x_array[num_points_per_elem * (e * dim + d) + 2] = d == 0 ? 0.25 : -0.25; in main()
32 x_array[num_points_per_elem * (e * dim + d) + 3] = 0.25; in main()
52 for (CeedInt e = 0; e < num_elem; e++) { in main() local
55 for (CeedInt d = 0; d < dim; d++) n_d[d] = num_elem_1d * (p - 1) + 1; in main()
57 CeedInt r_e = e; in main()
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/libCEED/examples/nek/bps/
H A Dbps.usr1 C Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors
2 C All Rights Reserved. See the top-level COPYRIGHT and NOTICE files for details.
4 C SPDX-License-Identifier: (BSD-2-Clause)
10 C_TESTARGS(name="BP1") -c {ceed_resource} -e bp1 -n 1 -b 4 -test
11 C_TESTARGS(name="BP3") -c {ceed_resource} -e bp3 -n 1 -b 4 -test
13 C-----------------------------------------------------------------------
44 g11 = (a22*a33-a23*a32)
45 g12 = (a13*a32-a33*a12)
46 g13 = (a12*a23-a22*a13)
48 g21 = (a23*a31-a21*a33)
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/libCEED/backends/sycl-ref/
H A Dceed-sycl-restriction.sycl.cpp1 // Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other
2 // CEED contributors. All Rights Reserved. See the top-level LICENSE and NOTICE
5 // SPDX-License-Identifier: BSD-2-Clause
11 #include <ceed/jit-tools.h>
16 #include "../sycl/ceed-sycl-compile.hpp"
17 #include "ceed-sycl-ref.hpp"
24 //------------------------------------------------------------------------------
25 // Restriction Kernel : L-vector -> E-vector, strided
26 //------------------------------------------------------------------------------
29 const CeedInt elem_size = impl->elem_size; in CeedElemRestrictionStridedNoTranspose_Sycl()
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/libCEED/doc/sphinx/source/
H A DlibCEEDapi.md5 (theoretical-framework)=
10 In particular, when high-order finite elements or spectral elements are used, the resulting sparse …
11 libCEED provides an interface for matrix-free operator description that enables efficient evaluatio…
15 We first define the $L^2$ inner product between real-valued functions
30 …$ represents all terms in {eq}`residual` which multiply the (possibly vector-valued) test function…
31 For an n-component problems in $d$ dimensions, $\bm f_0 \in \mathbb{R}^n$ and $\bm f_1 \in \mathbb{…
34 …dot represents contraction in just one, which should be clear from context, e.g., $\bm v \cdot \bm…
47 …er the mesh elements, mapping each element to a simple *reference* element (e.g. the unit square) …
51 …inuous ($H^1$) elements, where we use the notions **T-vector**, **L-vector**, **E-vector** and **Q…
55 - Subdomain restriction $\bm{P}$
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