version 0.0.1

examples/problems/poisson.py

@@ -0,0 +1,35 @@
+import numpy as np
+import torch
+
+from pina.problem import SpatialProblem
+from pina.operators import nabla
+from pina import Condition, Span
+
+
+class Poisson(SpatialProblem):
+
+    spatial_variables = ['x', 'y']
+    output_variables = ['u']
+    domain = Span({'x': [0, 1], 'y': [0, 1]})
+
+    def laplace_equation(input_, output_):
+        force_term = (torch.sin(input_['x']*torch.pi) *
+                      torch.sin(input_['y']*torch.pi))
+        return nabla(output_['u'], input_).flatten() - force_term
+
+    def nil_dirichlet(input_, output_):
+        value = 0.0
+        return output_['u'] - value
+
+    conditions = {
+        'gamma1': Condition(Span({'x': [-1, 1], 'y':  1}), nil_dirichlet),
+        'gamma2': Condition(Span({'x': [-1, 1], 'y': -1}), nil_dirichlet),
+        'gamma3': Condition(Span({'x':  1, 'y': [-1, 1]}), nil_dirichlet),
+        'gamma4': Condition(Span({'x': -1, 'y': [-1, 1]}), nil_dirichlet),
+        'D': Condition(Span({'x': [-1, 1], 'y': [-1, 1]}), laplace_equation),
+    }
+
+    def poisson_sol(self, x, y):
+        return -(np.sin(x*np.pi)*np.sin(y*np.pi))/(2*np.pi**2)
+
+    truth_solution = poisson_sol