.. only:: html .. _gallery-index: Gallery ======= Acoustics ^^^^^^^^^ .. list-table:: :align: center :class: gallery * - .. figure:: ../images/gallery/thumbnails/acoustics-acoustics.png :target: acoustics-acoustics.html :ref:`Acoustic pressure distribution ` - .. figure:: ../images/gallery/thumbnails/acoustics-acoustics3d_Omega_1.png :target: acoustics-acoustics3d.html :ref:`Acoustic pressure distribution in 3D ` - .. figure:: ../images/gallery/thumbnails/acoustics-helmholtz_apartment.png :target: acoustics-helmholtz_apartment.html :ref:`A script demonstrating the solution of the scalar Helmholtz equation for a situation inspired by the physical problem of WiFi propagation in an apartment ` * - .. figure:: ../images/gallery/thumbnails/acoustics-vibro_acoustic3d_Gamma0.png :target: acoustics-vibro_acoustic3d.html :ref:`Vibro-acoustic problem 3D acoustic domain with 2D perforated deforming interface ` - .. - .. Dg ^^ .. list-table:: :align: center :class: gallery * - .. figure:: ../images/gallery/thumbnails/dg-advection_1D.png :target: dg-advection_1D.html :ref:`Transient advection equation in 1D solved using discontinous galerkin method ` - .. - .. Diffusion ^^^^^^^^^ .. list-table:: :align: center :class: gallery * - .. figure:: ../images/gallery/thumbnails/diffusion-cube.png :target: diffusion-cube.html :ref:`Laplace equation (eg: temperature distribution) on a cube geometry with different boundary condition values on the cube sides ` - .. figure:: ../images/gallery/thumbnails/diffusion-darcy_flow_multicomp.png :target: diffusion-darcy_flow_multicomp.html :ref:`Each of the two equations describes a flow in one compartment of a porous medium ` - .. figure:: ../images/gallery/thumbnails/diffusion-laplace_1d.png :target: diffusion-laplace_1d.html :ref:`Laplace equation in 1D with a variable coefficient ` * - .. figure:: ../images/gallery/thumbnails/diffusion-laplace_coupling_lcbcs.png :target: diffusion-laplace_coupling_lcbcs.html :ref:`Two Laplace equations with multiple linear combination constraints ` - .. figure:: ../images/gallery/thumbnails/diffusion-laplace_fluid_2d.png :target: diffusion-laplace_fluid_2d.html :ref:`A Laplace equation that models the flow of "dry water" around an obstacle shaped like a Citroen CX ` - .. figure:: ../images/gallery/thumbnails/diffusion-laplace_iga_interactive.png :target: diffusion-laplace_iga_interactive.html :ref:`Laplace equation with Dirichlet boundary conditions solved in a single patch NURBS domain using the isogeometric analysis (IGA) approach, using commands for interactive use ` * - .. figure:: ../images/gallery/thumbnails/diffusion-laplace_refine_interactive.png :target: diffusion-laplace_refine_interactive.html :ref:`Example of solving Laplace's equation on a block domain refined with level 1 hanging nodes ` - .. figure:: ../images/gallery/thumbnails/diffusion-laplace_shifted_periodic.png :target: diffusion-laplace_shifted_periodic.html :ref:`Laplace equation with shifted periodic BCs ` - .. figure:: ../images/gallery/thumbnails/diffusion-laplace_time_ebcs.png :target: diffusion-laplace_time_ebcs.html :ref:`Example explaining how to change Dirichlet boundary conditions depending on time ` * - .. figure:: ../images/gallery/thumbnails/diffusion-poisson.png :target: diffusion-poisson.html :ref:`Laplace equation using the long syntax of keywords ` - .. figure:: ../images/gallery/thumbnails/diffusion-poisson_field_dependent_material.png :target: diffusion-poisson_field_dependent_material.html :ref:`Laplace equation with a field-dependent material parameter ` - .. figure:: ../images/gallery/thumbnails/diffusion-poisson_functions.png :target: diffusion-poisson_functions.html :ref:`Poisson equation with source term ` * - .. figure:: ../images/gallery/thumbnails/diffusion-poisson_iga.png :target: diffusion-poisson_iga.html :ref:`Poisson equation solved in a single patch NURBS domain using the isogeometric analysis (IGA) approach ` - .. figure:: ../images/gallery/thumbnails/diffusion-poisson_neumann.png :target: diffusion-poisson_neumann.html :ref:`The Poisson equation with Neumann boundary conditions on a part of the boundary ` - .. figure:: ../images/gallery/thumbnails/diffusion-poisson_nonlinear_material.png :target: diffusion-poisson_nonlinear_material.html :ref:`Nonlinear Poisson's equation example demonstrating the nonlinear diffusion and nonlinear volume force terms ` * - .. figure:: ../images/gallery/thumbnails/diffusion-poisson_parallel_interactive.png :target: diffusion-poisson_parallel_interactive.html :ref:`Parallel assembling and solving of a Poisson's equation, using commands for interactive use ` - .. figure:: ../images/gallery/thumbnails/diffusion-poisson_parametric_study.png :target: diffusion-poisson_parametric_study.html :ref:`Poisson equation ` - .. figure:: ../images/gallery/thumbnails/diffusion-poisson_periodic_boundary_condition.png :target: diffusion-poisson_periodic_boundary_condition.html :ref:`Transient Laplace equation with a localized power source and periodic boundary conditions ` * - .. figure:: ../images/gallery/thumbnails/diffusion-poisson_short_syntax.png :target: diffusion-poisson_short_syntax.html :ref:`Laplace equation using the short syntax of keywords ` - .. figure:: ../images/gallery/thumbnails/diffusion-sinbc_grad.png :target: diffusion-sinbc.html :ref:`Laplace equation with Dirichlet boundary conditions given by a sine function and constants ` - .. figure:: ../images/gallery/thumbnails/diffusion-time_advection_diffusion.png :target: diffusion-time_advection_diffusion.html :ref:`The transient advection-diffusion equation with a given divergence-free advection velocity ` * - .. figure:: ../images/gallery/thumbnails/diffusion-time_heat_equation_multi_material.png :target: diffusion-time_heat_equation_multi_material.html :ref:`Transient heat equation with time-dependent source term, three different material domains and Newton type boundary condition loss term ` - .. figure:: ../images/gallery/thumbnails/diffusion-time_poisson.png :target: diffusion-time_poisson.html :ref:`Transient Laplace equation with non-constant initial conditions given by a function ` - .. figure:: ../images/gallery/thumbnails/diffusion-time_poisson_explicit.png :target: diffusion-time_poisson_explicit.html :ref:`Transient Laplace equation ` * - .. figure:: ../images/gallery/thumbnails/diffusion-time_poisson_interactive-time_poisson_interactive_probe_04.png :target: diffusion-time_poisson_interactive.html :ref:`Transient Laplace equation (heat equation) with non-constant initial conditions given by a function, using commands for interactive use ` - .. - .. Homogenization ^^^^^^^^^^^^^^ .. list-table:: :align: center :class: gallery * - .. figure:: ../images/gallery/thumbnails/homogenization-linear_homogenization.png :target: homogenization-linear_homogenization.html :ref:`Compute homogenized elastic coefficients for a given heterogeneous linear elastic microstructure ` - .. figure:: ../images/gallery/thumbnails/homogenization-nonlinear_hyperelastic_mM.png :target: homogenization-nonlinear_hyperelastic_mM.html :ref:`Homogenized nonlinear hyperelastic material with evolving microstructure deformation in each macroscopic quadrature point ` - .. figure:: ../images/gallery/thumbnails/homogenization-perfusion_micro_etaA_YM.png :target: homogenization-perfusion_micro.html :ref:`Homogenization of the Darcy flow in a thin porous layer ` * - .. figure:: ../images/gallery/thumbnails/homogenization-rs_correctors.png :target: homogenization-rs_correctors.html :ref:`Compute homogenized elastic coefficients for a given microstructure ` - .. - .. Large Deformation ^^^^^^^^^^^^^^^^^ .. list-table:: :align: center :class: gallery * - .. figure:: ../images/gallery/thumbnails/large_deformation-active_fibres.png :target: large_deformation-active_fibres.html :ref:`Nearly incompressible hyperelastic material model with active fibres ` - .. figure:: ../images/gallery/thumbnails/large_deformation-balloon.png :target: large_deformation-balloon.html :ref:`Inflation of a Mooney-Rivlin hyperelastic balloon ` - .. figure:: ../images/gallery/thumbnails/large_deformation-compare_elastic_materials-pressure_displacement.png :target: large_deformation-compare_elastic_materials.html :ref:`Compare various elastic materials w ` * - .. figure:: ../images/gallery/thumbnails/large_deformation-gen_yeoh_tl_up_interactive-gen_yeoh_tl_up_comparison.png :target: large_deformation-gen_yeoh_tl_up_interactive.html :ref:`Incompressible generalized Yeoh hyperelastic material model ` - .. figure:: ../images/gallery/thumbnails/large_deformation-hyperelastic.png :target: large_deformation-hyperelastic.html :ref:`Nearly incompressible Mooney-Rivlin hyperelastic material model ` - .. figure:: ../images/gallery/thumbnails/large_deformation-hyperelastic_tl_up_interactive-hyperelastic_tl_up_comparison.png :target: large_deformation-hyperelastic_tl_up_interactive.html :ref:`Incompressible Mooney-Rivlin hyperelastic material model ` * - .. figure:: ../images/gallery/thumbnails/large_deformation-hyperelastic_ul.png :target: large_deformation-hyperelastic_ul.html :ref:`Nearly incompressible Mooney-Rivlin hyperelastic material model ` - .. figure:: ../images/gallery/thumbnails/large_deformation-hyperelastic_ul_up.png :target: large_deformation-hyperelastic_ul_up.html :ref:`Compressible Mooney-Rivlin hyperelastic material model ` - .. figure:: ../images/gallery/thumbnails/large_deformation-perfusion_tl.png :target: large_deformation-perfusion_tl.html :ref:`Porous nearly incompressible hyperelastic material with fluid perfusion ` Linear Elasticity ^^^^^^^^^^^^^^^^^ .. list-table:: :align: center :class: gallery * - .. figure:: ../images/gallery/thumbnails/linear_elasticity-dispersion_analysis-frequencies.png :target: linear_elasticity-dispersion_analysis.html :ref:`Dispersion analysis of a heterogeneous finite scale periodic cell ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-elastic_contact_planes.png :target: linear_elasticity-elastic_contact_planes.html :ref:`Elastic contact planes simulating an indentation test ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-elastic_contact_sphere.png :target: linear_elasticity-elastic_contact_sphere.html :ref:`Elastic contact sphere simulating an indentation test ` * - .. figure:: ../images/gallery/thumbnails/linear_elasticity-elastic_shifted_periodic.png :target: linear_elasticity-elastic_shifted_periodic.html :ref:`Linear elasticity with linear combination constraints and periodic boundary conditions ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-elastodynamic.png :target: linear_elasticity-elastodynamic.html :ref:`The linear elastodynamics solution of an iron plate impact problem ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-elastodynamic_identification-res00004.png :target: linear_elasticity-elastodynamic_identification.html :ref:`The linear elastodynamics solution of an iron plate impact problem with identification of material parameters from simulated measurement data ` * - .. figure:: ../images/gallery/thumbnails/linear_elasticity-its2D_1.png :target: linear_elasticity-its2D_1.html :ref:`Diametrically point loaded 2-D disk ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-its2D_2.png :target: linear_elasticity-its2D_2.html :ref:`Diametrically point loaded 2-D disk with postprocessing ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-its2D_3.png :target: linear_elasticity-its2D_3.html :ref:`Diametrically point loaded 2-D disk with nodal stress calculation ` * - .. figure:: ../images/gallery/thumbnails/linear_elasticity-its2D_4-its2D_0.png :target: linear_elasticity-its2D_4.html :ref:`Diametrically point loaded 2-D disk with postprocessing and probes ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-its2D_5-its2D_probe_line0.png :target: linear_elasticity-its2D_5.html :ref:`Diametrically point loaded 2-D disk with postprocessing and probes ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-its2D_interactive-its2D_interactive_probe_0.png :target: linear_elasticity-its2D_interactive.html :ref:`Diametrically point loaded 2-D disk, using commands for interactive use ` * - .. figure:: ../images/gallery/thumbnails/linear_elasticity-linear_elastic.png :target: linear_elasticity-linear_elastic.html :ref:`Linear elasticity with given displacements ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-linear_elastic_damping.png :target: linear_elasticity-linear_elastic_damping.html :ref:`Time-dependent linear elasticity with a simple damping ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-linear_elastic_iga.png :target: linear_elasticity-linear_elastic_iga.html :ref:`Linear elasticity solved in a single patch NURBS domain using the isogeometric analysis (IGA) approach ` * - .. figure:: ../images/gallery/thumbnails/linear_elasticity-linear_elastic_interactive.png :target: linear_elasticity-linear_elastic_interactive.html :ref:`Linear elasticity example using the imperative API ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-linear_elastic_probes-cylinder_probe_line.png :target: linear_elasticity-linear_elastic_probes.html :ref:`This example shows how to use the post_process_hook to probe the output data ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-linear_elastic_tractions.png :target: linear_elasticity-linear_elastic_tractions.html :ref:`Linear elasticity with pressure traction load on a surface and constrained to one-dimensional motion ` * - .. figure:: ../images/gallery/thumbnails/linear_elasticity-linear_elastic_up.png :target: linear_elasticity-linear_elastic_up.html :ref:`Nearly incompressible linear elasticity in mixed displacement-pressure formulation with comments ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-linear_viscoelastic.png :target: linear_elasticity-linear_viscoelastic.html :ref:`Linear viscoelasticity with pressure traction load on a surface and constrained to one-dimensional motion ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-material_nonlinearity.png :target: linear_elasticity-material_nonlinearity.html :ref:`Example demonstrating how a linear elastic term can be used to solve an elasticity problem with a material nonlinearity ` * - .. figure:: ../images/gallery/thumbnails/linear_elasticity-mixed_mesh.png :target: linear_elasticity-mixed_mesh.html :ref:`A linear elastic beam loaded with a continuous force ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-modal_analysis.png :target: linear_elasticity-modal_analysis.html :ref:`Modal analysis of a linear elastic block in 2D or 3D ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-modal_analysis_declarative.png :target: linear_elasticity-modal_analysis_declarative.html :ref:`Modal analysis of a wheel set ` * - .. figure:: ../images/gallery/thumbnails/linear_elasticity-nodal_lcbcs.png :target: linear_elasticity-nodal_lcbcs.html :ref:`Linear elasticity with nodal linear combination constraints ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-prestress_fibres.png :target: linear_elasticity-prestress_fibres.html :ref:`Linear elasticity with a given prestress in one subdomain and a (pre)strain fibre reinforcement in the other ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-seismic_load.png :target: linear_elasticity-seismic_load.html :ref:`The linear elastodynamics of an elastic body loaded by a given base motion ` * - .. figure:: ../images/gallery/thumbnails/linear_elasticity-shell10x_cantilever.png :target: linear_elasticity-shell10x_cantilever.html :ref:`Bending of a long thin cantilever beam, declarative problem description ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-shell10x_cantilever_interactive-shell10x_cantilever_convergence_bent.png :target: linear_elasticity-shell10x_cantilever_interactive.html :ref:`Bending of a long thin cantilever beam, imperative problem description ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-truss_bridge.png :target: linear_elasticity-truss_bridge.html :ref:`An example demonstrating the usage of the truss elements in 2D ` * - .. figure:: ../images/gallery/thumbnails/linear_elasticity-truss_bridge3d_Solid.png :target: linear_elasticity-truss_bridge3d.html :ref:`An example demonstrating the usage of the truss structural elements in 3D ` - .. figure:: ../images/gallery/thumbnails/linear_elasticity-two_bodies_contact.png :target: linear_elasticity-two_bodies_contact.html :ref:`Contact of two elastic bodies with a penalty function for enforcing the contact constraints ` - .. Miscellaneous ^^^^^^^^^^^^^ .. list-table:: :align: center :class: gallery * - .. figure:: ../images/gallery/thumbnails/miscellaneous-live_plot-live_plot.png :target: miscellaneous-live_plot.html :ref:`Live plot demonstration ` - .. figure:: ../images/gallery/thumbnails/miscellaneous-refine_evp-h-refinement-0-laplace-lagrange-primme-none-a.png :target: miscellaneous-refine_evp.html :ref:`Plot the convergence of eigenvalues (or corresponding frequencies) of an eigenvalue problem to an analytical solution, when applying the uniform mesh refinement ` - .. Multi Physics ^^^^^^^^^^^^^ .. list-table:: :align: center :class: gallery * - .. figure:: ../images/gallery/thumbnails/multi_physics-biot.png :target: multi_physics-biot.html :ref:`Biot problem - deformable porous medium ` - .. figure:: ../images/gallery/thumbnails/multi_physics-biot_npbc.png :target: multi_physics-biot_npbc.html :ref:`Biot problem - deformable porous medium with the no-penetration boundary condition on a boundary region ` - .. figure:: ../images/gallery/thumbnails/multi_physics-biot_npbc_lagrange.png :target: multi_physics-biot_npbc_lagrange.html :ref:`Biot problem - deformable porous medium with the no-penetration boundary condition on a boundary region enforced using Lagrange multipliers ` * - .. figure:: ../images/gallery/thumbnails/multi_physics-biot_parallel_interactive.png :target: multi_physics-biot_parallel_interactive.html :ref:`Parallel assembling and solving of a Biot problem (deformable porous medium), using commands for interactive use ` - .. figure:: ../images/gallery/thumbnails/multi_physics-biot_short_syntax.png :target: multi_physics-biot_short_syntax.html :ref:`Biot problem - deformable porous medium with a no-penetration boundary condition imposed in the weak sense on a boundary region, using the short syntax of keywords ` - .. figure:: ../images/gallery/thumbnails/multi_physics-piezo_elasticity.png :target: multi_physics-piezo_elasticity.html :ref:`Piezo-elasticity problem - linear elastic material with piezoelectric effects ` * - .. figure:: ../images/gallery/thumbnails/multi_physics-piezo_elasticity_macro.png :target: multi_physics-piezo_elasticity_macro.html :ref:`Piezo-elasticity problem - homogenization of a piezoelectric linear elastic matrix with embedded metalic electrodes, see [1] for details ` - .. figure:: ../images/gallery/thumbnails/multi_physics-piezo_elastodynamic.png :target: multi_physics-piezo_elastodynamic.html :ref:`The linear elastodynamics of a piezoelectric body loaded by a given base motion ` - .. figure:: ../images/gallery/thumbnails/multi_physics-thermal_electric.10.png :target: multi_physics-thermal_electric.html :ref:`First solve the stationary electric conduction problem ` * - .. figure:: ../images/gallery/thumbnails/multi_physics-thermo_elasticity.png :target: multi_physics-thermo_elasticity.html :ref:`Thermo-elasticity with a given temperature distribution ` - .. figure:: ../images/gallery/thumbnails/multi_physics-thermo_elasticity_ess.png :target: multi_physics-thermo_elasticity_ess.html :ref:`Thermo-elasticity with a computed temperature demonstrating equation sequence solver ` - .. Navier Stokes ^^^^^^^^^^^^^ .. list-table:: :align: center :class: gallery * - .. figure:: ../images/gallery/thumbnails/navier_stokes-navier_stokes.png :target: navier_stokes-navier_stokes.html :ref:`Navier-Stokes equations for incompressible fluid flow ` - .. figure:: ../images/gallery/thumbnails/navier_stokes-navier_stokes2d.png :target: navier_stokes-navier_stokes2d.html :ref:`Navier-Stokes equations for incompressible fluid flow in 2D ` - .. figure:: ../images/gallery/thumbnails/navier_stokes-navier_stokes2d_iga.png :target: navier_stokes-navier_stokes2d_iga.html :ref:`Navier-Stokes equations for incompressible fluid flow in 2D solved in a single patch NURBS domain using the isogeometric analysis (IGA) approach ` * - .. figure:: ../images/gallery/thumbnails/navier_stokes-stabilized_navier_stokes.png :target: navier_stokes-stabilized_navier_stokes.html :ref:`Stabilized Navier-Stokes problem with grad-div, SUPG and PSPG stabilization solved by a custom Oseen solver ` - .. figure:: ../images/gallery/thumbnails/navier_stokes-stokes.png :target: navier_stokes-stokes.html :ref:`Stokes equations for incompressible fluid flow ` - .. figure:: ../images/gallery/thumbnails/navier_stokes-stokes_slip_bc.png :target: navier_stokes-stokes_slip_bc.html :ref:`Incompressible Stokes flow with Navier (slip) boundary conditions, flow driven by a moving wall and a small diffusion for stabilization ` Phononic ^^^^^^^^ .. list-table:: :align: center :class: gallery * - .. figure:: ../images/gallery/thumbnails/phononic-band_gaps-band_gaps.png :target: phononic-band_gaps.html :ref:`Acoustic band gaps in a strongly heterogeneous elastic body, detected using homogenization techniques ` - .. figure:: ../images/gallery/thumbnails/phononic-band_gaps_rigid-band_gaps_rigid.png :target: phononic-band_gaps_rigid.html :ref:`Acoustic band gaps in a strongly heterogeneous elastic body with a rigid inclusion, detected using homogenization techniques ` - .. Quantum ^^^^^^^ .. list-table:: :align: center :class: gallery * - .. figure:: ../images/gallery/thumbnails/quantum-boron.png :target: quantum-boron.html :ref:`Boron atom with 1 electron ` - .. figure:: ../images/gallery/thumbnails/quantum-hydrogen.png :target: quantum-hydrogen.html :ref:`Hydrogen atom ` - .. figure:: ../images/gallery/thumbnails/quantum-oscillator.png :target: quantum-oscillator.html :ref:`Quantum oscillator ` * - .. figure:: ../images/gallery/thumbnails/quantum-well.png :target: quantum-well.html :ref:`Quantum potential well ` - .. - ..