Solver API

Unified API for PDE solving and visualization.

This module provides a clean, professional interface for solving different types of PDEs with flexible boundary conditions and initial conditions.

class pdevisualizer.solver.EquationType(value)[source]

Bases: Enum

Supported PDE types.

HEAT = 'heat'

WAVE = 'wave'

class pdevisualizer.solver.BoundaryCondition(boundary_type, value=0.0)[source]

Bases: object

Boundary condition specification - Enhanced version.

Methods

`absorbing`()	Absorbing boundary condition (for waves).
`dirichlet`([value])	Fixed value boundary condition.
`neumann`([flux])	Fixed flux boundary condition (insulated if flux=0).
`periodic`()	Periodic boundary condition.
`to_boundary_spec`()	Convert to BoundarySpec for the boundary_conditions module.

Parameters:

boundary_type (BoundaryType)
value (float)

classmethod dirichlet(value=0.0)[source]

Fixed value boundary condition.

Parameters:: value (float)

classmethod neumann(flux=0.0)[source]

Fixed flux boundary condition (insulated if flux=0).

Parameters:: flux (float)

classmethod periodic()[source]: Periodic boundary condition.

classmethod absorbing()[source]: Absorbing boundary condition (for waves).

to_boundary_spec()[source]: Convert to BoundarySpec for the boundary_conditions module.

class pdevisualizer.solver.InitialConditions[source]

Bases: object

Helper class for creating common initial conditions.

Methods

`circular_wave`(shape, center, radius[, amplitude])	Circular wave initial condition.
`constant`(shape, value)	Constant field initial condition.
`gaussian_pulse`(shape, center, sigma[, amplitude])	Gaussian pulse initial condition.
`multiple_sources`(shape, sources)	Multiple point sources initial condition.
`sine_wave`(shape, wavelength[, amplitude, ...])	Sinusoidal wave initial condition.
`zeros`(shape)	Zero initial condition.

static zeros(shape)[source]

Zero initial condition.

Parameters:: shape (Tuple[int, int])
Return type:: ndarray

static constant(shape, value)[source]

Constant field initial condition.

Parameters:

shape (Tuple[int, int])
value (float)

Return type:

ndarray

static gaussian_pulse(shape, center, sigma, amplitude=1.0)[source]

Gaussian pulse initial condition.

Parameters:

shape (Tuple[int, int])
center (Tuple[float, float])
sigma (float)
amplitude (float)

Return type:

ndarray

static circular_wave(shape, center, radius, amplitude=1.0)[source]

Circular wave initial condition.

Parameters:

shape (Tuple[int, int])
center (Tuple[float, float])
radius (float)
amplitude (float)

Return type:

ndarray

static multiple_sources(shape, sources)[source]

Multiple point sources initial condition.

Parameters:: shape (Tuple[int, int])
Return type:: ndarray

static sine_wave(shape, wavelength, amplitude=1.0, direction='x')[source]

Sinusoidal wave initial condition.

Parameters:

shape (Tuple[int, int])
wavelength (float)
amplitude (float)
direction (str)

Return type:

ndarray

class pdevisualizer.solver.PDESolver(equation, grid_shape=(100, 100), spacing=(1.0, 1.0), boundary=None)[source]

Bases: object

Unified interface for solving 2D partial differential equations.

This class provides a clean, professional API for solving heat and wave equations with flexible boundary conditions and initial conditions.

Methods

`animate`([frames, interval, save_path])	Create an animation of the PDE solution.
`get_stability_info`()	Get stability condition information for current parameters.
`info`()	Get a summary of the current solver configuration.
`set_initial_conditions`(u0[, v0])	Set initial conditions for the PDE.
`set_parameters`(**params)	Set equation-specific parameters.
`solve`([steps])	Solve the PDE for the specified number of time steps.
`validate_stability`()	Validate that current parameters satisfy stability conditions.

Initialize the PDE solver.

Methods

`animate`([frames, interval, save_path])	Create an animation of the PDE solution.
`get_stability_info`()	Get stability condition information for current parameters.
`info`()	Get a summary of the current solver configuration.
`set_initial_conditions`(u0[, v0])	Set initial conditions for the PDE.
`set_parameters`(**params)	Set equation-specific parameters.
`solve`([steps])	Solve the PDE for the specified number of time steps.
`validate_stability`()	Validate that current parameters satisfy stability conditions.

Parameters:

equation (str | EquationType)
grid_shape (Tuple[int, int])
spacing (Tuple[float, float])
boundary (BoundaryCondition | None)

__init__(equation, grid_shape=(100, 100), spacing=(1.0, 1.0), boundary=None)[source]

Initialize the PDE solver.

Parameters:

equation (str | EquationType)
grid_shape (Tuple[int, int])
spacing (Tuple[float, float])
boundary (BoundaryCondition | None)

set_initial_conditions(u0, v0=None)[source]

Set initial conditions for the PDE.

Parameters:

u0 (ndarray)
v0 (ndarray | None)

set_parameters(**params)[source]

Set equation-specific parameters.

For heat equation: alpha (thermal diffusivity), dt (time step) For wave equation: c (wave speed), dt (time step)

get_stability_info()[source]

Get stability condition information for current parameters.

Return type:: Dict[str, Any]

validate_stability()[source]: Validate that current parameters satisfy stability conditions.

solve(steps=100)[source]

Solve the PDE for the specified number of time steps.

Parameters:: steps (int)
Return type:: ndarray

animate(frames=100, interval=50, save_path=None)[source]

Create an animation of the PDE solution.

Parameters:

frames (int)
interval (int)
save_path (str | None)

Return type:

FuncAnimation

info()[source]

Get a summary of the current solver configuration.

Return type:: str

PDESolver Class

class pdevisualizer.solver.PDESolver(equation, grid_shape=(100, 100), spacing=(1.0, 1.0), boundary=None)[source]

Bases: object

Unified interface for solving 2D partial differential equations.

This class provides a clean, professional API for solving heat and wave equations with flexible boundary conditions and initial conditions.

Methods

`animate`([frames, interval, save_path])	Create an animation of the PDE solution.
`get_stability_info`()	Get stability condition information for current parameters.
`info`()	Get a summary of the current solver configuration.
`set_initial_conditions`(u0[, v0])	Set initial conditions for the PDE.
`set_parameters`(**params)	Set equation-specific parameters.
`solve`([steps])	Solve the PDE for the specified number of time steps.
`validate_stability`()	Validate that current parameters satisfy stability conditions.

Initialize the PDE solver.

Methods

`animate`([frames, interval, save_path])	Create an animation of the PDE solution.
`get_stability_info`()	Get stability condition information for current parameters.
`info`()	Get a summary of the current solver configuration.
`set_initial_conditions`(u0[, v0])	Set initial conditions for the PDE.
`set_parameters`(**params)	Set equation-specific parameters.
`solve`([steps])	Solve the PDE for the specified number of time steps.
`validate_stability`()	Validate that current parameters satisfy stability conditions.

Parameters:

equation (str | EquationType)
grid_shape (Tuple[int, int])
spacing (Tuple[float, float])
boundary (BoundaryCondition | None)

__init__(equation, grid_shape=(100, 100), spacing=(1.0, 1.0), boundary=None)[source]

Initialize the PDE solver.

Parameters:

equation (str | EquationType)
grid_shape (Tuple[int, int])
spacing (Tuple[float, float])
boundary (BoundaryCondition | None)

set_initial_conditions(u0, v0=None)[source]

Set initial conditions for the PDE.

Parameters:

u0 (ndarray)
v0 (ndarray | None)

set_parameters(**params)[source]

Set equation-specific parameters.

For heat equation: alpha (thermal diffusivity), dt (time step) For wave equation: c (wave speed), dt (time step)

get_stability_info()[source]

Get stability condition information for current parameters.

Return type:: Dict[str, Any]

validate_stability()[source]: Validate that current parameters satisfy stability conditions.

solve(steps=100)[source]

Solve the PDE for the specified number of time steps.

Parameters:: steps (int)
Return type:: ndarray

animate(frames=100, interval=50, save_path=None)[source]

Create an animation of the PDE solution.

Parameters:

frames (int)
interval (int)
save_path (str | None)

Return type:

FuncAnimation

info()[source]

Get a summary of the current solver configuration.

Return type:: str

EquationType

class pdevisualizer.solver.EquationType(value)[source]

Supported PDE types.

HEAT = 'heat'

WAVE = 'wave'

BoundaryCondition

class pdevisualizer.solver.BoundaryCondition(boundary_type, value=0.0)[source]

Boundary condition specification - Enhanced version.

Methods

`absorbing`()	Absorbing boundary condition (for waves).
`dirichlet`([value])	Fixed value boundary condition.
`neumann`([flux])	Fixed flux boundary condition (insulated if flux=0).
`periodic`()	Periodic boundary condition.
`to_boundary_spec`()	Convert to BoundarySpec for the boundary_conditions module.

Parameters:

boundary_type (BoundaryType)
value (float)

classmethod dirichlet(value=0.0)[source]

Fixed value boundary condition.

Parameters:: value (float)

classmethod neumann(flux=0.0)[source]

Fixed flux boundary condition (insulated if flux=0).

Parameters:: flux (float)

classmethod periodic()[source]: Periodic boundary condition.

classmethod absorbing()[source]: Absorbing boundary condition (for waves).

to_boundary_spec()[source]: Convert to BoundarySpec for the boundary_conditions module.

InitialConditions

class pdevisualizer.solver.InitialConditions[source]

Helper class for creating common initial conditions.

Methods

`circular_wave`(shape, center, radius[, amplitude])	Circular wave initial condition.
`constant`(shape, value)	Constant field initial condition.
`gaussian_pulse`(shape, center, sigma[, amplitude])	Gaussian pulse initial condition.
`multiple_sources`(shape, sources)	Multiple point sources initial condition.
`sine_wave`(shape, wavelength[, amplitude, ...])	Sinusoidal wave initial condition.
`zeros`(shape)	Zero initial condition.

static zeros(shape)[source]

Zero initial condition.

Parameters:: shape (Tuple[int, int])
Return type:: ndarray

static constant(shape, value)[source]

Constant field initial condition.

Parameters:

shape (Tuple[int, int])
value (float)

Return type:

ndarray

static gaussian_pulse(shape, center, sigma, amplitude=1.0)[source]

Gaussian pulse initial condition.

Parameters:

shape (Tuple[int, int])
center (Tuple[float, float])
sigma (float)
amplitude (float)

Return type:

ndarray

static circular_wave(shape, center, radius, amplitude=1.0)[source]

Circular wave initial condition.

Parameters:

shape (Tuple[int, int])
center (Tuple[float, float])
radius (float)
amplitude (float)

Return type:

ndarray

static multiple_sources(shape, sources)[source]

Multiple point sources initial condition.

Parameters:: shape (Tuple[int, int])
Return type:: ndarray

static sine_wave(shape, wavelength, amplitude=1.0, direction='x')[source]

Sinusoidal wave initial condition.

Parameters:

shape (Tuple[int, int])
wavelength (float)
amplitude (float)
direction (str)

Return type:

ndarray