Added Adams-Bashforth stepper

pde/solvers/__init__.py

@@ -9,6 +9,7 @@
    ~explicit_mpi.ExplicitMPISolver
    ~implicit.ImplicitSolver
    ~crank_nicolson.CrankNicolsonSolver
+   ~adams_bashforth.AdamsBashforthSolver
    ~scipy.ScipySolver
    ~registered_solvers
 
@@ -17,6 +18,7 @@
 
 from typing import List
 
+from .adams_bashforth import AdamsBashforthSolver
 from .controller import Controller
 from .crank_nicolson import CrankNicolsonSolver
 from .explicit import ExplicitSolver
@@ -46,6 +48,7 @@ def registered_solvers() -> list[str]:
     "ExplicitSolver",
     "ImplicitSolver",
     "CrankNicolsonSolver",
+    "AdamsBashforthSolver",
     "ScipySolver",
     "registered_solvers",
 ]

pde/solvers/adams_bashforth.py

@@ -0,0 +1,83 @@
+"""
+Defines an explicit solver supporting various methods
+   
+.. codeauthor:: David Zwicker <[email protected]> 
+"""
+
+from __future__ import annotations
+
+from typing import Callable
+
+import numba as nb
+import numpy as np
+
+from ..fields.base import FieldBase
+from ..tools.numba import jit
+from .base import SolverBase
+
+
+class AdamsBashforthSolver(SolverBase):
+    """solving partial differential equations using an Adams-Bashforth scheme"""
+
+    name = "adams–bashforth"
+
+    def _make_fixed_stepper(
+        self, state: FieldBase, dt: float
+    ) -> Callable[[np.ndarray, float, int], tuple[float, float]]:
+        """return a stepper function using an explicit scheme with fixed time steps
+
+        Args:
+            state (:class:`~pde.fields.base.FieldBase`):
+                An example for the state from which the grid and other information can
+                be extracted
+            dt (float):
+                Time step of the explicit stepping
+        """
+        if self.pde.is_sde:
+            raise NotImplementedError
+
+        rhs_pde = self._make_pde_rhs(state, backend=self.backend)
+        modify_state_after_step = self._modify_state_after_step
+        modify_after_step = self._make_modify_after_step(state)
+
+        def single_step(
+            state_data: np.ndarray, t: float, state_prev: np.ndarray
+        ) -> None:
+            """perform a single Adams-Bashforth step"""
+            rhs_prev = rhs_pde(state_prev, t - dt).copy()
+            rhs_cur = rhs_pde(state_data, t)
+            state_prev[:] = state_data  # save the previous state
+            state_data += dt * (1.5 * rhs_cur - 0.5 * rhs_prev)
+
+        # allocate memory to store the state of the previous time step
+        state_prev = np.empty_like(state.data)
+        init_state_prev = True
+
+        if self._compiled:
+            sig_single_step = (nb.typeof(state.data), nb.double, nb.typeof(state_prev))
+            single_step = jit(sig_single_step)(single_step)
+
+        def fixed_stepper(
+            state_data: np.ndarray, t_start: float, steps: int
+        ) -> tuple[float, float]:
+            """perform `steps` steps with fixed time steps"""
+            nonlocal state_prev, init_state_prev
+
+            if init_state_prev:
+                # initialize the state_prev with an estimate of the previous step
+                state_prev[:] = state_data - dt * rhs_pde(state_data, t_start)
+                init_state_prev = False
+
+            modifications = 0.0
+            for i in range(steps):
+                # calculate the right hand side
+                t = t_start + i * dt
+                single_step(state_data, t, state_prev)
+                if modify_state_after_step:
+                    modifications += modify_after_step(state_data)
+
+            return t + dt, modifications
+
+        self._logger.info("Init explicit Adams-Bashforth stepper with dt=%g", dt)
+
+        return fixed_stepper

tests/solvers/test_adams_bashforth_solver.py

@@ -0,0 +1,25 @@
+"""
+.. codeauthor:: David Zwicker <[email protected]>
+"""
+
+import numpy as np
+
+import pde
+
+
+def test_adams_bashforth():
+    """test the adams_bashforth method"""
+    eq = pde.PDE({"y": "y"})
+    state = pde.ScalarField(pde.UnitGrid([1]), 1)
+    storage = pde.MemoryStorage()
+    eq.solve(
+        state,
+        t_range=2.1,
+        dt=0.5,
+        solver="adams–bashforth",
+        tracker=storage.tracker(0.5),
+    )
+    np.testing.assert_allclose(
+        np.ravel([f.data for f in storage]),
+        [1, 13 / 8, 83 / 32, 529 / 128, 3371 / 512, 21481 / 2048],
+    )

tests/solvers/test_generic_solvers.py

@@ -7,6 +7,7 @@
 
 from pde import PDE, DiffusionPDE, FieldCollection, MemoryStorage, ScalarField, UnitGrid
 from pde.solvers import (
+    AdamsBashforthSolver,
     Controller,
     CrankNicolsonSolver,
     ExplicitSolver,
@@ -16,7 +17,13 @@
 )
 from pde.solvers.base import AdaptiveSolverBase
 
-SOLVER_CLASSES = [ExplicitSolver, ImplicitSolver, CrankNicolsonSolver, ScipySolver]
+SOLVER_CLASSES = [
+    ExplicitSolver,
+    ImplicitSolver,
+    CrankNicolsonSolver,
+    AdamsBashforthSolver,
+    ScipySolver,
+]
 
 
 def test_solver_registration():