WolframFEMA Core Part of
Wolfram Language

Finite Element Method.

For beginners to experts, Wolfram FEM captures the behavior of your design by providing multiphysics partial differential equation models, solvers and seamless post-processing functions, fully integrated with advanced geometry and visualization capabilities.

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Geometric Modeling

Design accurate simulations. Create multi-material geometric models using Boolean operations or implicit descriptions, or reconstruct them from point data, images, geographic maps and more. Import many CAD and other geometry file formats like STEP, DXF and STL.

Mesh Generation

For numerical computation, approximate geometries with generated or imported meshes. Specify refinements, create graded or mapped meshes, and add perfectly matched layers (PMLs) to match your application.

Heat Transfer

Compute heat transfer in multi-material, nonlinear, porous, anisotropic models with events or phase changes in fluids or in solids. Use a variety of boundary conditions, PMLs and source types for 1D, 2D, 3D and axisymmetric cases.

Fluid Dynamics

Analyze fluid flow. Solve the Stokes or Navier–Stokes equations in 2 or 3 dimensions. Model non-Newtonian flow, buoyancy-driven flow with the Boussinesq approximation or couple the Navier–Stokes equation with other fields of physics like heat transfer or mass transport.

Mass Transport

Model interphase or anisotropic mass transport with variable, nonlinear diffusion coefficients including chemical reactions with various sources and boundary conditions in 1D, 2D, 3D and axisymmetric cases.

Solid Mechanics

Compute displacement, reaction forces, strains and stresses. Use hyperelastic or linear and nonlinear elastic, anisotropic material models, possibly coupled. Perform static, time-dependent, parametric, frequency response, vibration or eigenmode analysis in 2D and 3D.

Acoustics

Model multi-material acoustics in the time or frequency domain. Perform harmonic or eigenfrequency analysis with a multitude of boundary conditions and sources. Use PMLs to get accurate solutions. Literally hear the difference in acoustics designs.

Electromagnetics

Explore and analyze electromagnetic devices, solving Maxwell’s equations. Model with electrostatics, steady currents, magnetostatics and electromagnetic waves in 2 or 3 dimensions to visualize fields or easily compute secondary quantities such as impedance, power and losses.

Multiphysics

Combine predefined physics models without buying additional packages. Rethink FEA by combining PDE analysis with Wolfram Image, Geography, Chemistry or Signal. Set up model coefficients from real-time sensor data or access curated data from a vast set of topics.

Guide to Multiphysics Examples

System Physics

Combine finite element models with System Modeler. Use PDE models to drive system models or vice versa. Model each component in a complex system to its appropriate level.

Seamless Workflow

Say farewell to time-consuming, multi-tool, fragmented workflows and interfaces. Keep every aspect of your work, from data acquisition to report generation, in the same notebook environment.

Equation Solvers

Perform nonlinear, stationary or time-dependent analysis with dedicated, multipurpose iterative and parallel, direct or out-of-core solvers, plus an eigenmode solver and a parametric solver. No restriction in the number of nodes or elements used. Nonlinear PDEs are automatically linearized.

FEM Programming API

Intercept and control every aspect of the FEM solving process at any stage, and even devise new algorithms for solving PDEs.

Live Playground

This is an interactive notebook—try making your own changes!

Continue exploring more examples:Things to Try

Wolfram FEM Documentation

Wolfram FEM is an integrated part of Wolfram Language. The full system contains over 6,000 built-in functions covering all areas of computation—all carefully integrated so they work perfectly together.

Wolfram Language
Full Scope & Documentation

D ▪ Derivative ▪ Grad ▪ Div ▪ Curl ▪ Laplacian ▪ NDSolve ▪ DSolve ▪ NDSolveValue ▪ ParametricNDSolve ▪ NDEigensystem ▪ NDEigenvalues ▪ NIntegrate ▪ DirichletCondition ▪ NeumannValue ▪ PeriodicBoundaryCondition ▪ AcousticPDEComponent ▪ AcousticAbsorbingValue ▪ AcousticImpedanceValue ▪ AcousticNormalVelocityValue ▪ AcousticPressureCondition ▪ AcousticRadiationValue ▪ AcousticSoundHardValue ▪ AcousticSoundSoftCondition ▪ HeatTransferPDEComponent ▪ HeatFluxValue ▪ HeatInsulationValue ▪ HeatOutflowValue ▪ HeatRadiationValue ▪ HeatTemperatureCondition ▪ HeatSymmetryValue ▪ HeatTransfreValue ▪ MassConcentrationCondition ▪ MassFluxValue ▪ MassImpermeableBoundaryValue ▪ MassOutflowValue ▪ MassSymmetryValue ▪ MassTransportPDEComponent ▪ MassTransferValue ▪ SolidMechanicsPDEComponent ▪ SolidMechanicsStrain ▪ SolidMechanicsStress ▪ SolidBoundaryLoadValue ▪ SolidDisplacementCondition ▪ SolidFixedCondition ▪ LaplacianPDETerm ▪ PoissonPDEComponent ▪ WavePDEComponent ▪ DiffusionPDETerm ▪ ConvectionPDETerm ▪ ReactionPDETerm ▪ SourcePDETerm ▪ DerivativePDETerm ▪ ConservativeConvectionPDETerm ▪ Line ▪ DiscretizedPDEData ▪ DiscretizedBoundaryConditionData ▪ BoundaryUnitNormal ▪ LinearSolve ▪ FunctionExpand ▪ DifferentialRootReduce ▪ RegionNearest ▪ RegionMeasure ▪ RegionCentroid ▪ RegionDistance ▪ Region ▪ CanonicalizeRegion ▪ Ball ▪ Simplex ▪ Hexahedron ▪ InfiniteLine ▪ CrossingPolygon ▪ RandomPolygon ▪ PolygonDecomposition ▪ Polyhedron ▪ Dodecahedron ▪ Icosahedron ▪ DualPolyhedron ▪ HighlightMesh ▪ MeshCellStyle ▪ MeshCellLabel ▪ RegionUnion ▪ TransformedRegion ▪ RegionIntersection ▪ BooleanRegion ▪ RegionBoundary ▪ DelaunayMesh ▪ VoronoiMesh ▪ ConvexHullMesh ▪ ArrayMesh ▪ ImageMesh ▪ RegionConvert ▪ DiscretizeGraphics ▪ BoundaryDiscretizeGraphics ▪ DiscretizeRegion ▪ BoundaryDiscretizeRegion ▪ PolyhedronData ▪ ExampleData ▪ GeoElevationData ▪ ChemicalData ▪ AnatomyData ▪ KnotData ▪ LaminaData ▪ SolidData ▪ PlaneCurveData ▪ SpaceCurveData ▪ SurfaceData ▪ Printout3D ▪ FindMeshDefects ▪ RepairMesh ▪ ShellRegion ▪ GeometricScene ▪ RandomInstance ▪ FindGeometricConjectures ▪ ElectricCurrentDensityValue ▪ MagneticPDEComponent ▪ Polygon ▪ DensityPlot ▪ VonMisesStress ▪ IdentityMatrix ▪ TransformationFunction ▪ TranslationTransform ▪ HoldAll ▪ Block ▪ Exclusions ▪ ParametricRegion ▪ BoundaryMeshRegion ▪ MaxRecursion ▪ Interpolation ▪ Quantile ▪ BesselJ ▪ EllipticE ▪ CDF ▪ NMinimize ▪ NSum ▪ AsymptoticIntegrate ▪ NLineIntegrate ▪ NSurfaceIntegrate ▪ NContourIntegrate ▪ NExpectation ▪ NProbability ▪ ArcLength ▪ Area ▪ Volume ▪ MomentOfInertia ▪ Eigenvalues ▪ Sort ▪ Eigensystem ▪ Indeterminate ▪ MaxCellMeasure ▪ SortBy ▪ ImplicitRegion ▪ Reals ▪ Complexes ▪ Element ▪ ParametricFunction ▪ SystemModelParametricSimulate ▪ ParametricNDSolveValue ▪ Vectors ▪ Matrices ▪ $Assumptions ▪ DiscreteVariables ▪ GeneratedParameters ▪ WeierstrassP ▪ Erf ▪ C ▪ Assumptions ▪ IncludeSingularSolutions ▪ ParametricPlot ▪ FinancialDerivative ▪ InverseLaplaceTransform ▪ Activate ▪ DSolveValue ▪ DFixedPoints ▪ DStabilityConditions ▪ GreenFunction ▪ CompleteIntegral ▪ RSolve ▪ TruncateSum ▪ WhenEvent ▪ Compiled ▪ EvaluationMonitor ▪ StartingStepSize ▪ StepMonitor ▪ None ▪ MachinePrecision ▪ NormFunction ▪ Infinity ▪ WorkingPrecision ▪ MaxSteps ▪ DependentVariables ▪ Automatic ▪ Method ▪ Disk ▪ InterpolationOrder ▪ All ▪ MaxStepFraction ▪ MaxStepSize ▪ Sign ▪ Abs ▪ SystemModel ▪ AccuracyGoal ▪ PrecisionGoal ▪ AsymptoticDSolveValue ▪ NSolve ▪ DifferentialRoot ▪ StreamPlot ▪ SystemModelSimulate ▪ ItoProcess ▪ SymbolicZerosArray ▪ Cross ▪ TensorExpand ▪ Listable ▪ TensorContract ▪ Dot ▪ DEigenvalues ▪ SymbolicIdentityArray ▪ Transpose ▪ CoordinateChartData ▪ NetPortGradient ▪ Residue ▪ VectorSymbol ▪ MatrixSymbol ▪ ArraySymbol ▪ NonConstants ▪ Gamma ▪ PolyGamma ▪ AiryAiPrime ▪ AiryBiPrime ▪ Zeta ▪ JacobiSN ▪ JacobiCD ▪ LogIntegral ▪ ExpIntegralEi ▪ SinIntegral ▪ ConditionalExpression ▪ RealAbs ▪ RealSign ▪ Floor ▪ Ceiling ▪ Equal ▪ SymmetrizedArray ▪ SparseArray ▪ FourierTransform ▪ ZTransform ▪ GeneratingFunction ▪ KroneckerDelta ▪ GammaDistribution ▪ EstimatedDistribution ▪ Limit ▪ N ▪ First ▪ Outer ▪ Join ▪ Dimensions ▪ HodgeDual ▪ Total ▪ ArcCurvature ▪ DEigensystem ▪ DiscreteShift ▪ Solve ▪ Piecewise ▪ Sin ▪ Dt ▪ DifferenceQuotient ▪ Minimize ▪ Maximize ▪ Integrate ▪ DifferenceDelta ▪ CoefficientArrays ▪ FractionalD ▪ CaputoD ▪ ImplicitD ▪ RegionQ ▪ False ▪ RegionPlot ▪ RegionPlot3D ▪ True ▪ FindGeometricTransform ▪ MeshRegion ▪ InitialSeeding ▪ InterpolatingFunction ▪ Plot3D ▪ Animate ▪ Inactivate ▪ Inactive ▪ HelmholtzPDEComponent ▪ SchrodingerPDEComponent ▪ ElectrostaticPDEComponent ▪ ElectricCurrentPDEComponent ▪ MagnetostaticPDEComponent ▪ ElectricPotentialCondition ▪ ElectricFluxDensityValue ▪ ElectricSymmetryValue ▪ MagneticPotentialCondition ▪ MagneticFluxDensityValue ▪ MagneticSymmetryValue ▪ FluidFlowPDEComponent ▪ HeatTransferValue ▪