build_pid_test.py

# from https://github.com/taichi-dev/taichi/issues/2102

import taichi as ti

ti.init(default_fp=ti.f64, arch=ti.gpu)

# Sparse Grids
# ---Params
dim = 2
invDx = 1.0 / 0.003
nGrid = ti.ceil(invDx)
grid_size = 4096
grid_block_size = 128
leaf_block_size = 16 if dim == 2 else 8
indices = ti.ij if dim == 2 else ti.ijk
# offset = tuple(-grid_size // 2 for _ in range(dim))
offset = tuple(0 for _ in range(dim))
# ---Grid Shapes and Pointers
grid = ti.root.pointer(indices, grid_size // grid_block_size)  # 32
block = grid.pointer(indices, grid_block_size // leaf_block_size)  # 8


pid = ti.field(int)
block.dynamic(ti.axes(dim), 1024 * 1024, chunk_size=leaf_block_size ** dim * 8).place(
    pid, offset=offset + (0,)
)


useSparse = True
grid_m1 = ti.field(
    dtype=float, shape=(nGrid, nGrid)
)  # grid node field 1 mass is nGrid x nGrid, each grid node has a mass for each field

if useSparse:
    grid_m1 = ti.field(dtype=float)
    grid2 = ti.root.pointer(indices, grid_size // grid_block_size)  # 32
    block2 = grid2.pointer(indices, grid_block_size // leaf_block_size)  # 8
    block2.dense(indices, leaf_block_size).place(grid_m1, offset=offset)

# Particle Structures
x = ti.Vector.field(dim, dtype=float)  # position
mp = ti.field(dtype=float)  # particle masses
particle = ti.root.dynamic(
    ti.i, 2 ** 27, 2 ** 19
)  # 2**20 causes problems in CUDA (maybe asking for too much space)
particle.place(x, mp)


@ti.func
def stencil_range():
    return ti.ndrange(*((3,) * dim))


def addParticles():
    N = 10
    w = 0.2
    dw = w / N
    for i in range(N):
        for j in range(N):
            x[i * 10 + j] = [0.4 + (i * dw), 0.4 + (j * dw)]
            mp[i * 10 + j] = 0.001


@ti.kernel
def build_pid():
    ti.block_dim(64)  # this sets the number of threads per block / block dimension
    for p in x:
        base = int(ti.floor(x[p] * invDx - 0.5))
        ti.append(pid.parent(), base - ti.Vector(offset), p)


@ti.kernel
def p2g():
    ti.block_dim(256)
    ti.no_activate(particle)
    particleCount = 0
    for I in ti.grouped(pid):
        # print(I)
        p = pid[I]
        particleCount += 1
        base = ti.floor(x[p] * invDx - 0.5).cast(int)
        for D in ti.static(range(dim)):
            base[D] = ti.assume_in_range(base[D], I[D], 0, 1)
        fx = x[p] * invDx - base.cast(float)
        w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2]
        # P2G for mass
        for offset in ti.static(ti.grouped(stencil_range())):
            # ti.Vector(offset).cast(float)
            # offset.cast(float)

            # Loop over grid node stencil
            gridIdx = base + offset
            weight = 1.0
            for d in ti.static(range(dim)):
                weight *= w[offset[d]][d]
            grid_m1[gridIdx] += (
                weight * mp[p]
            )  # add mass to active field for this particle
    print("particleCount", particleCount)


@ti.kernel
def momentumToVelocity():
    activeNodes = 0
    for I in ti.grouped(grid_m1):
        if grid_m1[I] > 0.0001:
            # print("I:", I, " m1:", grid_m1[I])
            activeNodes += 1
    print("activeNodes:", activeNodes)


addParticles()
grid.deactivate_all()
build_pid()
p2g()
momentumToVelocity()

mpm128_ggui_with_pid.py

import numpy as np

import taichi as ti

ti.init(arch=ti.gpu)  # Try to run on GPU

quality = 1  # Use a larger value for higher-res simulations
n_particles, n_grid = 9000 * quality ** 2, 128 * quality
dx, inv_dx = 1 / n_grid, float(n_grid)
dt = 1e-4 / quality
p_vol, p_rho = (dx * 0.5) ** 2, 1
p_mass = p_vol * p_rho
E, nu = 5e3, 0.2  # Young's modulus and Poisson's ratio
mu_0, lambda_0 = E / (2 * (1 + nu)), E * nu / (
    (1 + nu) * (1 - 2 * nu)
)  # Lame parameters

x = ti.Vector.field(2, dtype=float)  # , shape=n_particles)  # position
v = ti.Vector.field(2, dtype=float)  # , shape=n_particles)  # velocity
C = ti.Matrix.field(2, 2, dtype=float)  # , shape=n_particles)  # affine velocity field
F = ti.Matrix.field(2, 2, dtype=float)  # , shape=n_particles)  # deformation gradient
material = ti.field(dtype=int)  # , shape=n_particles)  # material id
Jp = ti.field(dtype=float)  # , shape=n_particles)  # plastic deformation

particle = ti.root.dense(ti.i, n_particles)
particle.place(x, v, C, F, material, Jp)

grid_v = ti.Vector.field(
    2, dtype=float, shape=(n_grid, n_grid)
)  # grid node momentum/velocity
grid_m = ti.field(dtype=float, shape=(n_grid, n_grid))  # grid node mass
gravity = ti.Vector.field(2, dtype=float, shape=())
attractor_strength = ti.field(dtype=float, shape=())
attractor_pos = ti.Vector.field(2, dtype=float, shape=())

group_size = n_particles // 3
water = ti.Vector.field(2, dtype=float, shape=group_size)  # position
jelly = ti.Vector.field(2, dtype=float, shape=group_size)  # position
snow = ti.Vector.field(2, dtype=float, shape=group_size)  # position
mouse_circle = ti.Vector.field(2, dtype=float, shape=(1,))


grid_block_size = 32
leaf_block_size = 8
# grid = ti.root.pointer(ti.ij, n_grid // grid_block_size)  # 32
# block = grid.pointer(ti.ij, grid_block_size // leaf_block_size)  # 8

block = ti.root.pointer(ti.ij, n_grid // leaf_block_size)  # 32

pid = ti.field(int)
dim = 2
# offset = tuple(0 for _ in range(dim))
block.dynamic(ti.axes(dim), 1024 * 1024, chunk_size=leaf_block_size ** 2 * 8).place(
    pid,
    # offset=offset + (0,)
)


@ti.kernel
def build_pid():
    ti.block_dim(64)  # this sets the number of threads per block / block dimension
    for p in x:
        # base = int(ti.floor(x[p] * inv_dx - 0.5))
        base = (x[p] * inv_dx - 0.5).cast(int)
        ti.append(pid.parent(), base, p)


@ti.kernel
def substep():

    for i, j in grid_m:
        grid_v[i, j] = [0, 0]
        grid_m[i, j] = 0
    ti.no_activate(particle)
    for I in ti.grouped(pid):
        p = pid[I]
        # for p in x:  # Particle state update and scatter to grid (P2G)
        base = (x[p] * inv_dx - 0.5).cast(int)
        fx = x[p] * inv_dx - base.cast(float)
        # Quadratic kernels  [http://mpm.graphics   Eqn. 123, with x=fx, fx-1,fx-2]
        w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2]
        F[p] = (ti.Matrix.identity(float, 2) + dt * C[p]) @ F[
            p
        ]  # deformation gradient update
        h = max(
            0.1, min(5, ti.exp(10 * (1.0 - Jp[p])))
        )  # Hardening coefficient: snow gets harder when compressed
        if material[p] == 1:  # jelly, make it softer
            h = 0.3
        mu, la = mu_0 * h, lambda_0 * h
        if material[p] == 0:  # liquid
            mu = 0.0
        U, sig, V = ti.svd(F[p])
        J = 1.0
        for d in ti.static(range(2)):
            new_sig = sig[d, d]
            if material[p] == 2:  # Snow
                new_sig = min(max(sig[d, d], 1 - 2.5e-2), 1 + 4.5e-3)  # Plasticity
            Jp[p] *= sig[d, d] / new_sig
            sig[d, d] = new_sig
            J *= new_sig
        if material[p] == 0:
            # Reset deformation gradient to avoid numerical instability
            F[p] = ti.Matrix.identity(float, 2) * ti.sqrt(J)
        elif material[p] == 2:
            # Reconstruct elastic deformation gradient after plasticity
            F[p] = U @ sig @ V.transpose()
        stress = 2 * mu * (F[p] - U @ V.transpose()) @ F[
            p
        ].transpose() + ti.Matrix.identity(float, 2) * la * J * (J - 1)
        stress = (-dt * p_vol * 4 * inv_dx * inv_dx) * stress
        affine = stress + p_mass * C[p]
        for i, j in ti.static(ti.ndrange(3, 3)):  # Loop over 3x3 grid node neighborhood
            offset = ti.Vector([i, j])
            dpos = (offset.cast(float) - fx) * dx
            weight = w[i][0] * w[j][1]
            grid_v[base + offset] += weight * (p_mass * v[p] + affine @ dpos)
            grid_m[base + offset] += weight * p_mass
    for i, j in grid_m:
        if grid_m[i, j] > 0:  # No need for epsilon here
            grid_v[i, j] = (1 / grid_m[i, j]) * grid_v[i, j]  # Momentum to velocity
            grid_v[i, j] += dt * gravity[None] * 30  # gravity
            dist = attractor_pos[None] - dx * ti.Vector([i, j])
            grid_v[i, j] += (
                dist / (0.01 + dist.norm()) * attractor_strength[None] * dt * 100
            )
            if i < 3 and grid_v[i, j][0] < 0:
                grid_v[i, j][0] = 0  # Boundary conditions
            if i > n_grid - 3 and grid_v[i, j][0] > 0:
                grid_v[i, j][0] = 0
            if j < 3 and grid_v[i, j][1] < 0:
                grid_v[i, j][1] = 0
            if j > n_grid - 3 and grid_v[i, j][1] > 0:
                grid_v[i, j][1] = 0

    for I in ti.grouped(pid):
        p = pid[I]
        # for p in x:  # grid to particle (G2P)
        base = (x[p] * inv_dx - 0.5).cast(int)
        fx = x[p] * inv_dx - base.cast(float)
        w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1.0) ** 2, 0.5 * (fx - 0.5) ** 2]
        new_v = ti.Vector.zero(float, 2)
        new_C = ti.Matrix.zero(float, 2, 2)
        for i, j in ti.static(ti.ndrange(3, 3)):  # loop over 3x3 grid node neighborhood
            dpos = ti.Vector([i, j]).cast(float) - fx
            g_v = grid_v[base + ti.Vector([i, j])]
            weight = w[i][0] * w[j][1]
            new_v += weight * g_v
            new_C += 4 * inv_dx * weight * g_v.outer_product(dpos)
        v[p], C[p] = new_v, new_C
        x[p] += dt * v[p]  # advection


@ti.kernel
def reset():
    for i in range(n_particles):
        x[i] = [
            ti.random() * 0.2 + 0.3 + 0.10 * (i // group_size),
            ti.random() * 0.2 + 0.05 + 0.32 * (i // group_size),
        ]
        material[i] = i // group_size  # 0: fluid 1: jelly 2: snow
        v[i] = [0, 0]
        F[i] = ti.Matrix([[1, 0], [0, 1]])
        Jp[i] = 1
        C[i] = ti.Matrix.zero(float, 2, 2)


@ti.kernel
def render():
    for i in range(group_size):
        water[i] = x[i]
        jelly[i] = x[i + group_size]
        snow[i] = x[i + 2 * group_size]


print(
    "[Hint] Use WSAD/arrow keys to control gravity. Use left/right mouse bottons to attract/repel. Press R to reset."
)

res = (512, 512)
window = ti.ui.Window("Taichi MLS-MPM-128", res=res, vsync=True)
canvas = window.get_canvas()
radius = 0.003

reset()
gravity[None] = [0, -1]

while window.running:
    if window.get_event(ti.ui.PRESS):
        if window.event.key == "r":
            reset()
        elif window.event.key in [ti.ui.ESCAPE]:
            break
    if window.event is not None:
        gravity[None] = [0, 0]  # if had any event
    if window.is_pressed(ti.ui.LEFT, "a"):
        gravity[None][0] = -1
    if window.is_pressed(ti.ui.RIGHT, "d"):
        gravity[None][0] = 1
    if window.is_pressed(ti.ui.UP, "w"):
        gravity[None][1] = 1
    if window.is_pressed(ti.ui.DOWN, "s"):
        gravity[None][1] = -1
    mouse = window.get_cursor_pos()
    mouse_circle[0] = ti.Vector([mouse[0], mouse[1]])
    canvas.circles(mouse_circle, color=(0.2, 0.4, 0.6), radius=0.05)
    attractor_pos[None] = [mouse[0], mouse[1]]
    attractor_strength[None] = 0
    if window.is_pressed(ti.ui.LMB):
        attractor_strength[None] = 1
    if window.is_pressed(ti.ui.RMB):
        attractor_strength[None] = -1

    for s in range(int(2e-3 // dt)):
        build_pid()
        substep()
    render()
    canvas.set_background_color((0.067, 0.184, 0.255))
    canvas.circles(water, radius=radius, color=(0, 0.5, 0.5))
    canvas.circles(jelly, radius=radius, color=(0.93, 0.33, 0.23))
    canvas.circles(snow, radius=radius, color=(1, 1, 1))
    window.show()