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Gallery¶

Acoustics¶

../_images/acoustics-acoustics1.png

Acoustic pressure distribution¶

../_images/acoustics-acoustics3d_Omega_11.png

Acoustic pressure distribution in 3D¶

../_images/acoustics-helmholtz_apartment1.png

A script demonstrating the solution of the scalar Helmholtz equation for a situation inspired by the physical problem of WiFi propagation in an apartment¶

../_images/acoustics-vibro_acoustic3d_Gamma01.png

Vibro-acoustic problem 3D acoustic domain with 2D perforated deforming interface¶

Dg¶

../_images/dg-advection_1D1.png

Transient advection equation in 1D solved using discontinous galerkin method¶

Diffusion¶

../_images/diffusion-cube1.png

Laplace equation (eg: temperature distribution) on a cube geometry with different boundary condition values on the cube sides¶

../_images/diffusion-darcy_flow_multicomp1.png

Each of the two equations describes a flow in one compartment of a porous medium¶

../_images/diffusion-laplace_1d1.png

Laplace equation in 1D with a variable coefficient¶

../_images/diffusion-laplace_coupling_lcbcs1.png

Two Laplace equations with multiple linear combination constraints¶

../_images/diffusion-laplace_fluid_2d1.png

A Laplace equation that models the flow of “dry water” around an obstacle shaped like a Citroen CX¶

../_images/diffusion-laplace_iga_interactive1.png

Laplace equation with Dirichlet boundary conditions solved in a single patch NURBS domain using the isogeometric analysis (IGA) approach, using commands for interactive use¶

../_images/diffusion-laplace_refine_interactive1.png

Example of solving Laplace’s equation on a block domain refined with level 1 hanging nodes¶

../_images/diffusion-laplace_shifted_periodic1.png

Laplace equation with shifted periodic BCs¶

../_images/diffusion-laplace_time_ebcs1.png

Example explaining how to change Dirichlet boundary conditions depending on time¶

../_images/diffusion-poisson1.png

Laplace equation using the long syntax of keywords¶

../_images/diffusion-poisson_field_dependent_material1.png

Laplace equation with a field-dependent material parameter¶

../_images/diffusion-poisson_functions1.png

Poisson equation with source term¶

../_images/diffusion-poisson_iga1.png

Poisson equation solved in a single patch NURBS domain using the isogeometric analysis (IGA) approach¶

../_images/diffusion-poisson_neumann1.png

The Poisson equation with Neumann boundary conditions on a part of the boundary¶

../_images/diffusion-poisson_nonlinear_material1.png

Nonlinear Poisson’s equation example demonstrating the nonlinear diffusion and nonlinear volume force terms¶

../_images/diffusion-poisson_parallel_interactive1.png

Parallel assembling and solving of a Poisson’s equation, using commands for interactive use¶

../_images/diffusion-poisson_parametric_study1.png

Poisson equation¶

../_images/diffusion-poisson_periodic_boundary_condition1.png

Transient Laplace equation with a localized power source and periodic boundary conditions¶

../_images/diffusion-poisson_short_syntax1.png

Laplace equation using the short syntax of keywords¶

../_images/diffusion-sinbc_grad1.png

Laplace equation with Dirichlet boundary conditions given by a sine function and constants¶

../_images/diffusion-time_advection_diffusion1.png

The transient advection-diffusion equation with a given divergence-free advection velocity¶

../_images/diffusion-time_heat_equation_multi_material1.png

Transient heat equation with time-dependent source term, three different material domains and Newton type boundary condition loss term¶

../_images/diffusion-time_poisson1.png

Transient Laplace equation with non-constant initial conditions given by a function¶

../_images/diffusion-time_poisson_explicit1.png

Transient Laplace equation¶

../_images/diffusion-time_poisson_interactive-time_poisson_interactive_probe_041.png

Transient Laplace equation (heat equation) with non-constant initial conditions given by a function, using commands for interactive use¶

Homogenization¶

../_images/homogenization-linear_homogenization.png

Compute homogenized elastic coefficients for a given heterogeneous linear elastic microstructure¶

../_images/homogenization-nonlinear_hyperelastic_mM.png

Homogenized nonlinear hyperelastic material with evolving microstructure deformation in each macroscopic quadrature point¶

../_images/homogenization-perfusion_micro_etaA_YM.png

Homogenization of the Darcy flow in a thin porous layer¶

../_images/homogenization-rs_correctors.png

Compute homogenized elastic coefficients for a given microstructure¶

Large Deformation¶

../_images/large_deformation-active_fibres.png

Nearly incompressible hyperelastic material model with active fibres¶

../_images/large_deformation-balloon.png

Inflation of a Mooney-Rivlin hyperelastic balloon¶

../_images/large_deformation-compare_elastic_materials-pressure_displacement.png

Compare various elastic materials w¶

../_images/large_deformation-gen_yeoh_tl_up_interactive-gen_yeoh_tl_up_comparison.png

Incompressible generalized Yeoh hyperelastic material model¶

../_images/large_deformation-hyperelastic.png

Nearly incompressible Mooney-Rivlin hyperelastic material model¶

../_images/large_deformation-hyperelastic_tl_up_interactive-hyperelastic_tl_up_comparison.png

Incompressible Mooney-Rivlin hyperelastic material model¶

../_images/large_deformation-hyperelastic_ul.png

Nearly incompressible Mooney-Rivlin hyperelastic material model¶

../_images/large_deformation-hyperelastic_ul_up.png

Compressible Mooney-Rivlin hyperelastic material model¶

../_images/large_deformation-perfusion_tl.png

Porous nearly incompressible hyperelastic material with fluid perfusion¶

Linear Elasticity¶

../_images/linear_elasticity-dispersion_analysis-frequencies.png

Dispersion analysis of a heterogeneous finite scale periodic cell¶

../_images/linear_elasticity-elastic_contact_planes.png

Elastic contact planes simulating an indentation test¶

../_images/linear_elasticity-elastic_contact_sphere.png

Elastic contact sphere simulating an indentation test¶

../_images/linear_elasticity-elastic_shifted_periodic.png

Linear elasticity with linear combination constraints and periodic boundary conditions¶

../_images/linear_elasticity-elastodynamic.png

The linear elastodynamics solution of an iron plate impact problem¶

../_images/linear_elasticity-elastodynamic_identification-res00004.png

The linear elastodynamics solution of an iron plate impact problem with identification of material parameters from simulated measurement data¶

../_images/linear_elasticity-its2D_1.png

Diametrically point loaded 2-D disk¶

../_images/linear_elasticity-its2D_2.png

Diametrically point loaded 2-D disk with postprocessing¶

../_images/linear_elasticity-its2D_3.png

Diametrically point loaded 2-D disk with nodal stress calculation¶

../_images/linear_elasticity-its2D_4-its2D_0.png

Diametrically point loaded 2-D disk with postprocessing and probes¶

../_images/linear_elasticity-its2D_5-its2D_probe_line0.png

Diametrically point loaded 2-D disk with postprocessing and probes¶

../_images/linear_elasticity-its2D_interactive-its2D_interactive_probe_0.png

Diametrically point loaded 2-D disk, using commands for interactive use¶

../_images/linear_elasticity-linear_elastic.png

Linear elasticity with given displacements¶

../_images/linear_elasticity-linear_elastic_damping.png

Time-dependent linear elasticity with a simple damping¶

../_images/linear_elasticity-linear_elastic_iga.png

Linear elasticity solved in a single patch NURBS domain using the isogeometric analysis (IGA) approach¶

../_images/linear_elasticity-linear_elastic_interactive.png

Linear elasticity example using the imperative API¶

../_images/linear_elasticity-linear_elastic_probes-cylinder_probe_line.png

This example shows how to use the post_process_hook to probe the output data¶

../_images/linear_elasticity-linear_elastic_tractions.png

Linear elasticity with pressure traction load on a surface and constrained to one-dimensional motion¶

../_images/linear_elasticity-linear_elastic_up.png

Nearly incompressible linear elasticity in mixed displacement-pressure formulation with comments¶

../_images/linear_elasticity-linear_viscoelastic.png

Linear viscoelasticity with pressure traction load on a surface and constrained to one-dimensional motion¶

../_images/linear_elasticity-material_nonlinearity.png

Example demonstrating how a linear elastic term can be used to solve an elasticity problem with a material nonlinearity¶

../_images/linear_elasticity-mixed_mesh.png

A linear elastic beam loaded with a continuous force¶

../_images/linear_elasticity-modal_analysis.png

Modal analysis of a linear elastic block in 2D or 3D¶

../_images/linear_elasticity-modal_analysis_declarative.png

Modal analysis of a wheel set¶

../_images/linear_elasticity-multi_node_lcbcs.png

Linear elasticity with multi node linear combination constraints¶

../_images/linear_elasticity-multi_point_constraints.png

The linear elasticity of two discs connected using multi-point constraints¶

../_images/linear_elasticity-nodal_lcbcs.png

Linear elasticity with nodal linear combination constraints¶

../_images/linear_elasticity-prestress_fibres.png

Linear elasticity with a given prestress in one subdomain and a (pre)strain fibre reinforcement in the other¶

../_images/linear_elasticity-seismic_load.png

The linear elastodynamics of an elastic body loaded by a given base motion¶

../_images/linear_elasticity-shell10x_cantilever.png

Bending of a long thin cantilever beam, declarative problem description¶

../_images/linear_elasticity-shell10x_cantilever_interactive-shell10x_cantilever_convergence_bent.png

Bending of a long thin cantilever beam, imperative problem description¶

../_images/linear_elasticity-truss_bridge.png

An example demonstrating the usage of the truss elements in 2D¶

../_images/linear_elasticity-truss_bridge3d_Solid.png

An example demonstrating the usage of the truss structural elements in 3D¶

../_images/linear_elasticity-two_bodies_contact.png

Contact of two elastic bodies with a penalty function for enforcing the contact constraints¶

../_images/linear_elasticity-wedge_mesh.png

A linear elastic beam loaded with a continuous force¶

Miscellaneous¶

../_images/miscellaneous-live_plot-live_plot.png

Live plot demonstration¶

../_images/miscellaneous-refine_evp-h-refinement-0-laplace-lagrange-primme-none-a.png

Plot the convergence of eigenvalues (or corresponding frequencies) of an eigenvalue problem to an analytical solution, when applying the uniform mesh refinement¶

Multi Physics¶

../_images/multi_physics-biot.png

Biot problem - deformable porous medium¶

../_images/multi_physics-biot_npbc.png

Biot problem - deformable porous medium with the no-penetration boundary condition on a boundary region¶

../_images/multi_physics-biot_npbc_lagrange.png

Biot problem - deformable porous medium with the no-penetration boundary condition on a boundary region enforced using Lagrange multipliers¶

../_images/multi_physics-biot_parallel_interactive.png

Parallel assembling and solving of a Biot problem (deformable porous medium), using commands for interactive use¶

../_images/multi_physics-biot_short_syntax.png

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¶

../_images/multi_physics-piezo_elasticity.png

Piezo-elasticity problem - linear elastic material with piezoelectric effects¶

../_images/multi_physics-piezo_elasticity_macro.png

Piezo-elasticity problem - homogenization of a piezoelectric linear elastic matrix with embedded metalic electrodes, see [1] for details¶

../_images/multi_physics-piezo_elastodynamic.png

The linear elastodynamics of a piezoelectric body loaded by a given base motion¶

../_images/multi_physics-thermal_electric.10.png

First solve the stationary electric conduction problem¶

../_images/multi_physics-thermo_elasticity.png

Thermo-elasticity with a given temperature distribution¶

../_images/multi_physics-thermo_elasticity_ess.png

Thermo-elasticity with a computed temperature demonstrating equation sequence solver¶

Navier Stokes¶

../_images/navier_stokes-navier_stokes.png

Navier-Stokes equations for incompressible fluid flow¶

../_images/navier_stokes-navier_stokes2d.png

Navier-Stokes equations for incompressible fluid flow in 2D¶

../_images/navier_stokes-navier_stokes2d_iga.png

Navier-Stokes equations for incompressible fluid flow in 2D solved in a single patch NURBS domain using the isogeometric analysis (IGA) approach¶

../_images/navier_stokes-stabilized_navier_stokes.png

Stabilized Navier-Stokes problem with grad-div, SUPG and PSPG stabilization solved by a custom Oseen solver¶

../_images/navier_stokes-stokes.png

Stokes equations for incompressible fluid flow¶

../_images/navier_stokes-stokes_slip_bc.png

Incompressible Stokes flow with Navier (slip) boundary conditions, flow driven by a moving wall and a small diffusion for stabilization¶

Phononic¶

../_images/phononic-band_gaps-band_gaps.png

Acoustic band gaps in a strongly heterogeneous elastic body, detected using homogenization techniques¶

../_images/phononic-band_gaps_rigid-band_gaps_rigid.png

Acoustic band gaps in a strongly heterogeneous elastic body with a rigid inclusion, detected using homogenization techniques¶

Quantum¶

../_images/quantum-boron.png

Boron atom with 1 electron¶

../_images/quantum-hydrogen.png

Hydrogen atom¶

../_images/quantum-oscillator.png

Quantum oscillator¶

../_images/quantum-well.png

Quantum potential well¶

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