Initial release

engine/plugins/solvers/gl2s.lua

@@ -0,0 +1,60 @@
+-- gl2s.lua: Gauss-Legendre 2-stage implicit Runge-Kutta (4th order, 6 NFE)
+-- A-stable, symplectic. Fixed-point iteration solves the implicit system.
+
+solver = {
+    name        = "gl2s",
+    display     = "Gauss-Legendre 2s (6 NFE)",
+    description = "Implicit 4th-order A-stable symplectic integrator",
+    nfe         = 6,
+    order       = 4,
+    needs_model = true,
+    stateful    = false,
+    stochastic  = false,
+}
+
+-- Butcher tableau
+local SQRT3_6 = 0.28867513459481287
+local C1  = 0.5 - SQRT3_6  -- ≈ 0.2113
+local C2  = 0.5 + SQRT3_6  -- ≈ 0.7887
+local A11 = 0.25
+local A12 = 0.25 - SQRT3_6  -- ≈ -0.0387
+local A21 = 0.25 + SQRT3_6  -- ≈ 0.5387
+local A22 = 0.25
+local ITERATIONS = 3
+
+function step(xt, vt, t_curr, t_prev, n, model_fn, vt_buf)
+    local dt = t_curr - t_prev
+
+    -- Initialize k1 = k2 = vt
+    local k1 = {}
+    local k2 = {}
+    for i = 0, n-1 do k1[i] = vt[i]; k2[i] = vt[i] end
+
+    local xt_orig = {}
+    for i = 0, n-1 do xt_orig[i] = xt[i] end
+
+    local t1 = t_curr - C1 * dt
+    local t2 = t_curr - C2 * dt
+
+    -- Fixed-point iteration
+    for iter = 1, ITERATIONS do
+        -- Stage 1: x1 = xt - dt*(A11*k1 + A12*k2)
+        for i = 0, n-1 do
+            xt[i] = xt_orig[i] - dt * (A11 * k1[i] + A12 * k2[i])
+        end
+        model_fn(xt, t1)
+        for i = 0, n-1 do k1[i] = vt_buf[i] end
+
+        -- Stage 2: x2 = xt - dt*(A21*k1 + A22*k2)
+        for i = 0, n-1 do
+            xt[i] = xt_orig[i] - dt * (A21 * k1[i] + A22 * k2[i])
+        end
+        model_fn(xt, t2)
+        for i = 0, n-1 do k2[i] = vt_buf[i] end
+    end
+
+    -- Final: xt = xt_orig - dt * 0.5 * (k1 + k2)
+    for i = 0, n-1 do
+        xt[i] = xt_orig[i] - dt * 0.5 * (k1[i] + k2[i])
+    end
+end