FlexPDE Help
Getting Started
Installation
Starting FlexPDE
FlexPDE Working Files
The Main Menu Bar
The File Menu
The Controls Menu
The Stop Menu
The Tool Bar
Editing Descriptor Files
Domain Review
While the Problem Runs
When the Problem Finishes
Viewing Saved Graphic Files
Preferences Window
General Settings Tab
Font Settings Tab
Web Proxy Settings Tab
License Registration Tab
Registering FlexPDE
Internet Key Registration
Dongle Registration
Network Dongle Registration
Software Key Registration
User Guide
Overview
What Is FlexPDE?
What Can FlexPDE Do?
How Does It Do It?
Who Can Use FlexPDE?
What Does A Script Look Like?
What About Boundary Conditions?
Basic Usage
How Do I Set Up My Problem?
Problem Setup Guidelines
Notation
Variables and Equations
Mapping the Domain
An Example Problem
Generating A Mesh
Defining Material Parameters
Setting the Boundary Conditions
Requesting Graphical Output
Putting It All Together
Interpreting a Script
Some Common Variations
Controlling Accuracy
Computing Integrals
Reporting Numerical Results
Summarizing Numerical Results
Parameter Studies Using STAGES
Cylindrical Geometry
Integrals In Cylindrical Geometry
A Cylindrical Example
Time Dependence
Bad Things To Do In Time Dependent Problems
Eigenvalues and Modal Analysis
The Eigenvalue Summary
Addressing More Difficult Problems
Nonlinear Coefficients and Equations
Complications Associated with Nonlinear Problems
Natural Boundary Conditions
Some Typical Cases
An Example of a Flux Boundary Condition
Discontinuous Variables
Contact Resistance
Decoupling
Using JUMP in problems with many variables
Using FlexPDE in One-Dimensional Problems
Using FlexPDE in Three-Dimensional Problems
The Concept of Extrusion
Extrusion Notation in FlexPDE
Layering
Setting Material Properties by Region and Layer
More Complex Extrusions
Void Compartments
Limited Regions
Specifying Plots on Cut Planes
The Complete 3D Canister
Setting Boundary Conditions in 3D
Shaped Layer Interfaces
Surface-Generating Functions
Integrals in Three Dimensions
More Advanced Plot Controls
3D Mesh Generation
Complex Variables
The Time-Sinusoidal Heat
Interpreting Time-Sinusoidal Results
Vector Variables
Curvilinear Coordinates
Magnetic Vector Potential
Variables Inactive in Some Regions
A Chemical Beaker
Variables Explicit in Some Regions
Moving Meshes
Mesh Balancing
The Pulsating Blob
Mesh Reconnection
Controlling Mesh Density
Post-processing with FlexPDE
Exporting Data to Other Applications
Importing Data from Other Applications
Using ARRAYS and MATRICES
Solving Nonlinear Problems
Using Multiple Processors
Running FlexPDE from the Command Line
Running FlexPDE Without A Graphical Interface
Importing DXF Files
Importing OBJ Files
Getting Help
Problem Descriptor Reference
Introduction
Preparing a Descriptor File
File Names and Extensions
Problem Descriptor Structure
Problem Descriptor Format
Case Sensitivity
"Include" Files
A Simple Example
The Elements of a Descriptor
Comments
Reserved Words and Symbols
Separators
Literal Strings
Numeric Constants
Built-in Functions
Analytic Functions
Non-Analytic Functions
Unit Functions
String Functions
The FIT Function
The LUMP Function
The RAMP Function
The SAVE Function
The SUM Function
The SWAGE Function
The VAL and EVAL functions
Boundary Search Functions
Operators
Arithmetic Operators
Complex Operators
Differential Operators
Integral Operators
Time Integrals
Line Integrals
2D Surface Integrals
3D Surface Integrals
2D Volume Integrals
3D Volume Integrals
Relational Operators
String Operators
Vector Operators
Tensor Operators
Predefined Elements
Expressions
Repeated Text
The Sections of a Descriptor
Title
Select
Mesh Generation Controls
Solution Controls
Global Graphics Controls
Coordinates
Variables
The THRESHOLD Clause
The ORDER Clause
Complex Variables
Moving Meshes
Variable Arrays
Vector Variables
Global Variables
Definitions
ARRAY Definitions
MATRIX Definitions
COMPLEX Definitions
Function Definitions
STAGED Definitions
POINT Definitions
TABLE Import Definitions
The TABLE Input function
The TABLEDEF input statement
TABLE Modifiers
TABLE File format
TABULATE definitions
TRANSFER Import Definitions
The PASSIVE Modifier
Mesh Control Parameters
Materials
Boundary Conditions
Initial Values
Equations
Association between Equations, Variables and Boundary Conditions
Sequencing of Equations
Initial Equations
Eigenvalues and Modal Analysis
Moving Meshes
Constraints
Extrusion
Rotation
Boundaries
Points
Boundary Paths
Regions
Reassigning Regional Parameters
Regions in One Dimension
Regions in Three Dimensions
Regional Parameter Values in 3D
Limited Regions in 3D
Empty Layers in 3D
Excludes
Features
Node Points
Ordering Regions
Numbering Regions
Fillets and Bevels
Specifying Boundary Conditions
Syntax of Boundary Condition Statements
Point Boundary Conditions
Boundary conditions in 1D
Boundary Conditions in 3D
Jump Boundaries
Periodic Boundaries
Complex and Vector Boundary Conditions
Front
Maximize
Minimize
Resolve
Time
Monitors and Plots
Graphics Display Specifications
Graphic Display Modifiers
Controlling the Plot Domain
Reports
The ERROR Variable
Window Tiling
Monitors in Steady State Problems
Monitors and Plots in Time Dependent Problems
Hardcopy
Graphics Export
Data Export
Data Export Specifications
TRANSFER File format
TRANSFER6 File format
Examples
Histories
End
Batch Processing
Technical Notes
Applications in Electromagnetics
Introduction
Finite Element Methods
Principles
Boundary Conditions
Integration by Parts and Natural Boundary Conditions
Adaptive Mesh Refinement
Time Integration
Summary
Electrostatics
Electrostatic Fields in 2D
Electrostatics in 3D
Capacitance per Unit Length in 2D Geometry
Magnetostatics
A Magnet Coil in 2D Cylindrical Coordinates
Nonlinear Permeability in 2D
Divergence Form
Boundary Conditions
Magnetic Materials in 3D
Waveguides
Homogeneous Waveguides
TE and TM Modes
Non-Homogeneous Waveguides
Boundary Conditions
Material Interfaces
References
Natural Boundary Conditions
Solving Nonlinear Problems
Avoid Discontinuities!
Smoothing Operators in PDE's
Interpreting Error Estimates
Coordinate Scaling
Making Movies
Converting from Version 4 to Version 5
Converting from Version 5 to Version 6
Converting from Version 6 to Version 7
How FlexPDE Works
Sample Problems
Applications
Chemistry
chemburn
melting
reaction
Control
control_steady
control_transient
Electricity
3d_capacitor
3d_capacitor_check
3d_dielectric
capacitance
dielectric
fieldmap
plate_capacitor
space_charge
Fluids
1d_eulerian_shock
1d_lagrangian_shock
2d_eulerian_shock
2d_piston_movingmesh
3d_flowbox
airfoil
black_oil
buoyant
buoyant+time
cavity_1k
channel
contaminant_transport
coupled_contaminant
coupled_contaminant_initeq
flowslab
geoflow
hyperbolic
landfill_gas_flow
lowvisc
swirl
viscous
Groundwater
porous
richards
water
Heatflow
1d_float_zone
3d_bricks
3d_bricks+time
axisymmetric_heat
float_zone
heat_boundary
radiation_flow
radiative_boundary
slider
Lasers
laser_heatflow
self_focus
Magnetism
3d_helmholtz_coil
3d_magnetron
3d_vector_magnetron
magnet_coil
permanent_magnet
saturation
Misc
diffusion
minimal_surface
surface_fit
Quantun_Mechanics
1d_finite_potential_well
2d_finite_potential_well
morse_potential
Stress
3d_bimetal
anisotropic_stress
axisymmetric_stress
bentbar
bentbar_moving
elasticity
fixed_plate
free_plate
harmonic
plasticity
prestube
tension
vibrate
Usage
1D
1d_cylinder
1d_cylinder_transient
1d_float_zone
1d_slab
1d_sphere
3D_domains
2d_sphere_in_cylinder
3d_box_in_sphere
3d_cocktail
3d_cylspec
3d_ellipsoid
3d_ellipsoid_shell
3d_extrusion_spec
3d_fillet
3d_guitar
3d_helix_layered
3d_helix_wrapped
3d_lenses
3d_limited_region
3d_pinchout
3d_pipes
3d_planespec
3d_pyramid
3d_shell
3d_shells
3d_sphere
3d_spherebox
3d_spherespec
3d_spool
3d_thermocouple
3d_toggle
3d_torus
3d_torus_tube
3d_twist
3d_void
off_axis_disks_2
off_axis_disks_3
regional_surfaces
tabular_surfaces
two_spheres
twoz_direct
twoz_import
twoz_export
twoz_planar
3D_Rotations
Rotated_heat_ring
Accuracy
forever
gaus1d
gaus2d
gaus3d
rotating_shape
sine1d
sine2d
sine3d
Arrays+Matrices
arrays
array_boundary
matrices
matrix_boundary
wave_boundary
CAD_Import
arrow_OBJimport
boxinbox_OBJimport
canincan_OBJimport
cube_OBJimport
cube2_OBJimport
cube2_validate
cubes_bigsmall_OBJimport
cubes_bigsmall_validate
gourd_OBJimport
helix_OBJimport
horn_OBJimport
torus_OBJimport
tubefaces_OBJimport
wineglass_OBJimport
Constraints
3d_constraint
3d_surf_constraint
boundary_constraint
constraint
Contact_Boundaries
3d_contact
3d_contact_region
contact_resistance_heating
thermal_contact_resistance
transient_contact_resistance_heating
Coordinate_Scaling
scaled_z
unscaled_z
Eigenvalues
3d_oildrum
3d_plate
drumhead
drumhole
drumhole_animate
filledguide
shiftguide
vibar
waveguide
waveguide20
Functions
complex_functions
floor_ceiling
function_definition
error_reporting
globalmax
globalmax_3d
standard_functions
sum
swage_pulse
swage_test
unit_functions
vector_functions
Implicit_Curves
implicit_curve_boundary
implicit_curve_surface
sine_boundary
sine_boundary_3d
Import_Export
3d_mesh_export
3d_mesh_import
3d_post_processing
3d_surf_export
blocktable
export
export_format
export_history
mesh_export
mesh_import
post_processing
smoothtable
splinetable
table
tabledef
table_export
table_import
transfer_export
transfer_import
Integrals
2d_integrals
3d_integrals
time_integral
Mesh_Control
3d_curvature
boundary_density
boundary_spacing
front
mesh_density
mesh_spacing
resolve
Misc
askuser
bc_sets
bc_switching
data_fitting
edge_distance
fillet
fit+weight
ifthen
lump
material_sets
moving_source
point_load
polar_coordinates
regional_equations
repeat
rotated_ellipse
save
spacetime1
spacetime2
spline_boundary
staged_geometry
stages
tabulate
tensors
two_histories
Moving_Mesh
1d_stretch_x
2d_blob_position
2d_blob_velocity
2d_bubble_reconnect
2d_lagrangian_shock
2d_movepoint
2d_stretch_x
2d_stretch_xy
3d_blob_position
3d_blob_velocity
3d_bubble_reconnect
3d_intrusion_reconnect
gaussian_valve_reconnect
sliptube_explicit_reconnect
ODE
linearode
nonlinode
second_order_time
Optimization
criticality
criticality_size
power_control
size_control
Periodicity
1d_periodic
2d_wave_propagation
3d_antiperiodic
3d_periodic_exchange
3d_xperiodic
3d_zperiodic
antiperiodic
azimuthal_periodic
periodic+time
periodic
periodic_contaminant
periodic_map
three-way_periodic_3d
two-way_periodic
two-way_periodic_3d
Plotting
3d_ploton
export_test
plot_on_grid
plot_test
Sequenced_Equations
equation_iteration
initialeq
smoothing_discontinuities
theneq+time
theneq
Stop+Restart
restart_export
restart_import
Variable_Types
array_variables
complex_emw21
complex_sinusoidal_heat
complex_variables
complex+time
inactive_variables
vector_lowvisc
vector_variables
vector+time
Release Notes