All the dependencies required to build the code are included. It should work on Windows, macOS and Linux, and it should build out of the box with CMake:
mkdir build
cd build
cmake ..
make -j4
On Linux you need zenity for the file dialog window to work. On macOS and Windows it should use the native windows directly.
Note that the formula for higher order bases and quadrature points are pre-computed using Python. CMake can call those python as part of the compilation process, but by default this automatic generation is disabled, since it requires a working python installation and additional packages (sympy and quadpy).
The main executable, ./Polyfem_bin, can be called with a GUI or through a command-line interface. The GUI is pretty simple and should be self-explanatory. To call the command-line interface, set the mesh path in the file example.json, and run as follows:
./Polyfem_bin --cmd --json ../example.json
For the complete list of options use
./Polyfem_bin -h
Complete example
{
"mesh": " ", "Mesh path"
"bc_tag": " ", "Path to the boundary tag file, each face/edge is associated with an unique number (you can use bc_setter for setting them in 3d)"
"normalize_mesh": true, "Normalize mesh such that it fits in the [0,1] bounding box"
"n_refs": 0, "Number of uniform refinement"
"refinenemt_location": 0.5, "Refiniement location of polyhedra"
"scalar_formulation": "Laplacian",
"tensor_formulation": "LinearElasticity",
"mixed_formulation": "Stokes",
"count_flipped_els": false, "Count (or not) flipped elements"
"iso_parametric": false, "Force isoparametric elements"
"discr_order": 1, "Dicretization order, supports P1, P2, P3, P4, Q1, Q2"
"pressure_discr_order": 1, "Pressure dicrezation order, for mixed formulation"
"output": "", "Output json path"
"problem": "Franke", "Problem to solve"
"problem_params": {}, "Problem specific parameters"
"n_boundary_samples": 6, "number of boundary samples (Dirichelt) or quadrature points (Neumann)"
"quadrature_order": 4, "quadrature order"
"export": { "Export options"
"full_mat": "", "Stiffnes matrix without boundary conditions"
"iso_mesh": "", "Isolines mesh"
"nodes": "", "FE nodes"
"solution": "", "Solution vector"
"spectrum": false, "Spectrum of the stiffness matrix"
"stiffness_mat": "", "Stiffmess matrix after setting boundary conditions"
"vis_boundary_only": false, "Exports only the boundary of volumetric meshes"
"vis_mesh": "", "Path for the vtu mesh"
"wire_mesh": "" "Wireframe of the mesh"
},
"use_spline": false, "Use spline for quad/hex elements"
"fit_nodes": false, "Fit nodes for spline basis"
"integral_constraints": 2, "Number of constraints for polygonal basis 0, 1, or 2"
"n_harmonic_samples": 10, "Number of face/line samples for harmonic bases for polyhedra"
"B": 3, "User provided parameter for pref tolerance"
"use_p_ref": false, "Enable prefinement for badly shaped simplices"
"discr_order_max": 4, "Maximum allowed dicrezation oder, used in p pref"
"h1_formula": false, "Use pref formula for h1 bound"
"force_linear_geometry": false, "Force Linear geometric maps"
"solver_type": "Pardiso", "Library for linear solver"
"precond_type": "Eigen::DiagonalPreconditioner",
"solver_params": {}, "solver specific parameters"
"nl_solver": "newton", "Non linear solver"
"line_search": "armijo", "Line search for newton solver"
"nl_solver_rhs_steps": 1, "Number of incremental load steps"
"save_solve_sequence": false, "Save all incremental load steps"
"params": { "Material parameter"
"k": 1.0, "Constant in helmolz"
"elasticity_tensor": {}, "Elasticity tensor, used in hooke and saint ventant"
"E": 1.5, "Young modulus"
"nu": 0.3, "Poisson's ratio"
"lambda": 0.329670329, "Lame parameter, E, nu have priority"
"mu": 0.384615384,
},
"tend": 1, "End time for time dependent simulations"
"time_steps": 10, "Number of time steps for time dependent simulations"
"vismesh_rel_area": 1e-05 "Relative resolution of the output mesh"
}-
scalar_formulation: Helmholtz, Laplacian
-
tensor_formulation: HookeLinearElasticity, LinearElasticity, NeoHookean, Ogden, SaintVenant
-
mixed_formulation: IncompressibleLinearElasticity, Stokes
-
problem: CompressionElasticExact, Cubic, DrivenCavity, Elastic, ElasticExact, ElasticZeroBC, Flow, Franke, GenericTensor, Gravity, Kernel, Linear, LinearElasticExact, MinSurf, PointBasedTensor, Quadratic, QuadraticElasticExact, Sine, TestProblem, TimeDependentFlow, TimeDependentScalar, TorsionElastic, Zero_BC
-
solver_type: Eigen::BiCGSTAB, Eigen::ConjugateGradient, Eigen::GMRES, Eigen::MINRES, Eigen::SimplicialLDLT, Eigen::SparseLU, Hypre,Pardiso
-
nl_solver: lbfgs, newton
-
line_search: armijo, armijo_alt, bisection, more_thuente
Each problem has a specific set of optional problem_params described here.
Has exact solution: true
Time dependent: false
Form: tensor
Description: solve for
f_{2D}(x,y) = -[(y^3 + x^2 + xy)/20, (3x^4 + xy^2 + x)/20]
f_{3D}(x,y,z) = -[(xy + x^2 + y^3 + 6z)/14, (zx - z^3 + xy^2 + 3x^4)/14, (xyz + y^2z^2 - 2x)/14]
Has exact solution: true
Time dependent: false
Form: scalar
Description: solve for
f(x,y,z) = (2y-0.9)^4 + 0.1
Has exact solution: false
Time dependent: false
Form: mixed
Description: solve for zero right-hand side, and 0.25 for boundary id 1
Has exact solution: false
Time dependent: false
Form: tensor
Description: solve for zero right-hand side, -0.25 for boundary id 1/5, 0.25 for id 3/6
Has exact solution: true
Time dependent: false
Form: tensor
Description: solve for
f_{2D}(x,y) = [(y^3 + x^2 + xy)/50, (3x^4 + xy^2 + x)/50]
f_{3D}(x,y,z) = [(xy + x^2 + y^3 + 6z)/80, (xz - z^3 + xy^2 + 3x^4)/80, (xyz + y^2 z^2 - 2x)/80]
Has exact solution: false
Time dependent: false
Form: tensor
Description: solve for [0, 0.5, 0] right-hand side and zero boundary condition
Has exact solution: false
Time dependent: false
Form: mixed
Description: solve for zero right-hand side, [0.25, 0, 0] for boundary id 1/3, [0, 0, 0] for 7
Has exact solution: true
Time dependent: false
Form: scalar
Description: solves for the 2D and 3D Franke function
Has exact solution: false
Time dependent: false
Form: tesor
Description: solves for generic tensor problem with zero body forces
Options:
"use_mixed_formulation": false, "Use mixed formulation"
"dirichlet_boundary": [ "List of Dirichelt boundaries"
{
"id": 1, "Boundary id"
"value": [0, 0, 0], "Boundary vector value"
"dimension": [ "Which dimension are Dirichelt"
true,
true,
false "In this case z is free"
]
},
{
"id": 2, "Boundary id"
"value": ["sin(x)+y", "z^2", 0],"Formulas are supported"
}],
"neumann_boundary": [ "List of Neumann boundaries"
{
"id": 3, "Boundary id"
"value": [0, 0, 0], "Boundary vector value"
},
{
"id": 4, "Boundary id"
"value": ["sin(x)+y", "z^2", 0],"Formulas are supported"
}]Has exact solution: false
Time dependent: true
Form: tensor
Description: solves for 0.1 body force in y direction and zeor for boundray 4
Has exact solution: true
Time dependent: false
Form: scalar/tensor
Description: solves the omogenous PDE with n_kernels kernels placed on the bounding box at kernel_distance
Options: n_kernels sets the number of kernels, kernel_distance sets the distance from the bounding box
Has exact solution: true
Time dependent: false
Form: scalar
Description: solve for
f(x,y,z) = x
Has exact solution: true
Time dependent: false
Form: tensor
Description: solve for
f_{2D}(x,y) = [-(y + x)/50, -(3x + y)/50]
f_{3D}(x,y,z) = [-(y + x + z)/50, -(3x + y - z)/50, -(x + y - 2z)/50]
Has exact solution: false
Time dependent: false
Form: scalar
Description: solve for -10 for rhs, and zero Dirichelt boundary condition
Has exact solution: false
Time dependent: false
Form: tesor
Description: solves for point-based boudary conditions
Options:
"scaling": 1, "Scaling factor"
"rhs": 0, "Right-hand side"
"translation": [0, 0, 0] "Translation"
"boundary_ids": [ "List of Dirichelt boundaries"
{
"id": 1, "Boundary id"
"value": [0, 0, 0] "Boundary vector value"
},
{
"id": 2,
"value": { "Rbf interpolated value"
"function": "", "Function file"
"points": "", "Points file"
"rbf": "gaussian", "Rbf kernel"
"epsilon": 1.5, "Rbf epsilon"
"coordinate": 2, "Coordinate to ignore"
"dimension": [ "Which dimension are Dirichelt"
true,
true,
false "In this case z is free"
]
}
},
,
{
"id": 2,
"value": { "Rbf interpolated value"
"function": "", "Function file"
"points": "", "Points file"
"triangles": "", "Triangles file"
"coordinate": 2, "Coordinate to ignore"
}
}]Has exact solution: true
Time dependent: false
Form: scalar
Description: solve for
f(x,y,z) = x^2
Has exact solution: true
Time dependent: false
Form: tensor
Description: solve for
f_{2D}(x,y) = [-(y^2 + x^2 + xy)/50, -(3x^2 + y)/50]
f_{3D}(x,y,z) = [-(y^2 + x^2 + xy + yz)/50, -(3x^2 + y + z^2)/50, -(xz + y^2 - 2z)/50]
Has exact solution: true
Time dependent: false
Form: scalar
Description: solve for
f(x,y) = \sin(10x)\sin(10y)br/>
f(x,y,z) = \sin(10x)\sin(10y)\sin(10z)
Has exact solution: true
Time dependent: false
Form: scalar
Description: solve for extreme problem to test errors for high order discretizations
Has exact solution: false
Time dependent: true
Form: mixed
Description: solve for zero right-hand side, [0.25, 0, 0] for boundary id 1/3, [0, 0, 0] for 7, and zero inital velocity
Has exact solution: false
Time dependent: true
Form: scalar
Description: solve for one right-hand side, zero boundary condition, and zero time boundary
Has exact solution: false
Time dependent: false
Form: tensor
Description: solve for zero body forces, fixed_boundary fixed (zero displacement), turning_boundary rotating around axis_coordiante for n_turns
Options: fixed_boundary id of the fixed boundary, turning_boundary id of the moving boundary, axis_coordiante coordinate of the rotating axis, n_turns number of turns
Has exact solution: true
Time dependent: false
Form: tensor
Description: solve for
f_{2D}(x,y) = (1 - x) x^2 y (1-y)^2
f_{3D}(x,y,z) = (1 - x) x^2 y (1-y)^2 z (1 - z)