sin_cos.py

# Example file for the poisson problem
# Path: examples/poisson.py
# file contains the exact solution, rhs and boundary conditions for the poisson problem
import numpy as np
import tensorflow as tf


def left_boundary(x, y):
    """
    This function will return the boundary value for given component of a boundary
    """
    val = 0.0
    return np.ones_like(x) * val


def right_boundary(x, y):
    """
    This function will return the boundary value for given component of a boundary
    """
    val = 0.0
    return np.ones_like(x) * val


def top_boundary(x, y):
    """
    This function will return the boundary value for given component of a boundary
    """
    val = 0.0
    return np.ones_like(x) * val


def bottom_boundary(x, y):
    """
    This function will return the boundary value for given component of a boundary
    """
    val = 0.0
    return np.ones_like(x) * val


def rhs(x, y):
    """
    This function will return the value of the rhs at a given point
    """
    # f_temp =  32 * (x  * (1 - x) + y * (1 - y))
    # f_temp = 1
    # For a Laplace Equation, Make the f_temp = np.ones_like(x) * 0.0

    omegaX = 4.0 * np.pi
    omegaY = 4.0 * np.pi
    f_temp = -2.0 * (omegaX**2) * (np.sin(omegaX * x) * np.sin(omegaY * y))

    return f_temp


def exact_solution(x, y):
    """
    This function will return the exact solution at a given point
    """
    # If the exact Solution does not have an analytical expression, leave the value as 0(zero)
    # it can be set using `np.ones_like(x) * 0.0` and then ignore the errors and the error plots generated.

    omegaX = 4.0 * np.pi
    omegaY = 4.0 * np.pi
    val = -1.0 * np.sin(omegaX * x) * np.sin(omegaY * y)

    return val


def get_boundary_function_dict():
    """
    This function will return a dictionary of boundary functions
    """
    return {1000: bottom_boundary, 1001: right_boundary, 1002: top_boundary, 1003: left_boundary}


def get_bound_cond_dict():
    """
    This function will return a dictionary of boundary conditions
    """
    return {1000: "dirichlet", 1001: "dirichlet", 1002: "dirichlet", 1003: "dirichlet"}


def get_bilinear_params_dict():
    """
    This function will return a dictionary of bilinear parameters
    """
    eps = 1.0

    return {"eps": eps}