init

src/solvers/implicit.py

@@ -0,0 +1,95 @@
+import numpy as np
+import scipy.sparse
+import scipy.sparse.linalg
+
+import consts
+
+
+#@cachier(stale_after=datetime.timedelta(hours=1))
+def solve_implicit(grid) -> np.ndarray:
+  ug = np.zeros((grid.K + 1, grid.I + 1), dtype=float)
+
+  ug[0, :] = np.sin(np.pi * grid.xs / consts.l) ** 2 * 4 / 10
+
+  for k in range(1, grid.K + 1):
+    diags = {
+      -1: np.zeros(grid.I + 1, dtype=float),
+      0: np.zeros(grid.I + 1, dtype=float),
+      +1: np.zeros(grid.I + 1, dtype=float),
+    }
+    b = np.zeros(grid.I + 1, dtype=float)
+
+    # left
+    diags[0][0] = consts.H * grid.h_x + 1
+    diags[+1][0] = -1
+
+    # middle
+    for i in range(1, grid.I):
+      diags[-1][i] = grid.gamma
+      diags[0][i] = - 2 * grid.gamma - 1
+      diags[+1][i] = grid.gamma
+      b[i] = -ug[k - 1, i]
+
+    # right
+    diags[-1][grid.I] = -1
+    diags[0][grid.I] = consts.H * grid.h_x + 1
+
+    A = scipy.sparse.diags([
+      diags[-1][1:],
+      diags[0],
+      diags[+1][:-1],
+    ], [-1, 0, 1], format='csc')
+
+    ug[k, :] = scipy.sparse.linalg.spsolve(A, b)
+
+  return ug
+
+
+#@cachier(stale_after=datetime.timedelta(hours=1))
+def solve_implicit_improved(grid) -> np.ndarray:
+  ug = np.zeros((grid.K + 1, grid.I + 1), dtype=float)
+
+  ug[0, :] = np.sin(np.pi * grid.xs / consts.l) ** 2 * 4 / 10
+
+  for k in range(1, grid.K + 1):
+    diags = {
+      -1: np.zeros(grid.I + 1, dtype=float),
+      0: np.zeros(grid.I + 1, dtype=float),
+      +1: np.zeros(grid.I + 1, dtype=float),
+    }
+    b = np.zeros(grid.I + 1, dtype=float)
+
+    # left
+    diags[0][0] = (
+        2 * consts.H * grid.gamma * grid.h_x +
+        2 * grid.gamma +
+        1
+    )
+    diags[+1][0] = - 2 * grid.gamma
+    b[0] = ug[k - 1, 0]
+
+    # middle
+    for i in range(1, grid.I):
+      diags[-1][i] = grid.gamma
+      diags[0][i] = - 2 * grid.gamma - 1
+      diags[+1][i] = grid.gamma
+      b[i] = -ug[k - 1, i]
+
+    # right
+    diags[0][grid.I] = (
+        2 * consts.H * grid.gamma * grid.h_x +
+        2 * grid.gamma +
+        1
+    )
+    diags[-1][grid.I] = - 2 * grid.gamma
+    b[grid.I] = ug[k - 1, grid.I]
+
+    A = scipy.sparse.diags([
+      diags[-1][1:],
+      diags[0],
+      diags[+1][:-1],
+    ], [-1, 0, 1], format='csc')
+
+    ug[k, :] = scipy.sparse.linalg.spsolve(A, b)
+
+  return ug