50 lines
2.1 KiB
Python
50 lines
2.1 KiB
Python
import numpy as np
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import torch
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from pina.problem import Problem
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from pina.segment import Segment
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from pina.cube import Cube
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from pina.problem2d import Problem2D
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xmin, xmax, ymin, ymax = -1, 1, -1, 1
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class EllipticOptimalControl(Problem2D):
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def __init__(self, alpha=1):
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def term1(input_, output_):
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grad_p = self.grad(output_.extract(['p']), input_)
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gradgrad_p_x1 = self.grad(grad_p.extract(['x1']), input_)
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gradgrad_p_x2 = self.grad(grad_p.extract(['x2']), input_)
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yd = 2.0
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return output_.extract(['y']) - yd - (gradgrad_p_x1.extract(['x1']) + gradgrad_p_x2.extract(['x2']))
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def term2(input_, output_):
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grad_y = self.grad(output_.extract(['y']), input_)
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gradgrad_y_x1 = self.grad(grad_y.extract(['x1']), input_)
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gradgrad_y_x2 = self.grad(grad_y.extract(['x2']), input_)
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return - (gradgrad_y_x1.extract(['x1']) + gradgrad_y_x2.extract(['x2'])) - output_.extract(['u'])
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def term3(input_, output_):
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return output_.extract(['p']) - output_.extract(['u'])*alpha
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def nil_dirichlet(input_, output_):
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y_value = 0.0
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p_value = 0.0
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return torch.abs(output_.extract(['y']) - y_value) + torch.abs(output_.extract(['p']) - p_value)
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self.conditions = {
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'gamma1': {'location': Segment((xmin, ymin), (xmax, ymin)), 'func': nil_dirichlet},
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'gamma2': {'location': Segment((xmax, ymin), (xmax, ymax)), 'func': nil_dirichlet},
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'gamma3': {'location': Segment((xmax, ymax), (xmin, ymax)), 'func': nil_dirichlet},
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'gamma4': {'location': Segment((xmin, ymax), (xmin, ymin)), 'func': nil_dirichlet},
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'D1': {'location': Cube([[xmin, xmax], [ymin, ymax]]), 'func': [term1, term2, term3]},
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#'D2': {'location': Cube([[0, 1], [0, 1]]), 'func': term2},
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#'D3': {'location': Cube([[0, 1], [0, 1]]), 'func': term3}
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}
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self.input_variables = ['x1', 'x2']
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self.output_variables = ['u', 'p', 'y']
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self.spatial_domain = Cube([[xmin, xmax], [xmin, xmax]])
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