func compensateLRSurfaceCharges(m *data.Mesh, mxLeft, mxRight float64, bsat float64) *data.Slice {
h := data.NewSlice(3, m.Size())
H := h.Vectors()
world := m.WorldSize()
cell := m.CellSize()
size := m.Size()
q := cell[Z] * cell[Y] * bsat
q1 := q * mxLeft
q2 := q * (-mxRight)
prog, maxProg := 0, (size[Z]+1)*(size[Y]+1)
// surface loop (source)
for I := 0; I < size[Z]; I++ {
for J := 0; J < size[Y]; J++ {
prog++
util.Progress(prog, maxProg, "removing surface charges")
y := (float64(J) + 0.5) * cell[Y]
z := (float64(I) + 0.5) * cell[Z]
source1 := [3]float64{0, y, z} // left surface source
source2 := [3]float64{world[X], y, z} // right surface source
// volume loop (destination)
for iz := range H[0] {
for iy := range H[0][iz] {
for ix := range H[0][iz][iy] {
dst := [3]float64{ // destination coordinate
(float64(ix) + 0.5) * cell[X],
(float64(iy) + 0.5) * cell[Y],
(float64(iz) + 0.5) * cell[Z]}
h1 := hfield(q1, source1, dst)
h2 := hfield(q2, source2, dst)
// add this surface charges' field to grand total
for c := 0; c < 3; c++ {
H[c][iz][iy][ix] += float32(h1[c] + h2[c])
}
}
}
}
}
}
return h
}
// Calculates the magnetostatic kernel by brute-force integration
// of magnetic charges over the faces and averages over cell volumes.
func CalcDemagKernel(inputSize, pbc [3]int, cellsize [3]float64, accuracy float64) (kernel [3][3]*data.Slice) {
// Add zero-padding in non-PBC directions
size := padSize(inputSize, pbc)
// Sanity check
{
util.Assert(size[Z] > 0 && size[Y] > 0 && size[X] > 0)
util.Assert(cellsize[X] > 0 && cellsize[Y] > 0 && cellsize[Z] > 0)
util.Assert(pbc[X] >= 0 && pbc[Y] >= 0 && pbc[Z] >= 0)
util.Assert(accuracy > 0)
}
// Allocate only upper diagonal part. The rest is symmetric due to reciprocity.
var array [3][3][][][]float32
for i := 0; i < 3; i++ {
for j := i; j < 3; j++ {
kernel[i][j] = data.NewSlice(1, size)
array[i][j] = kernel[i][j].Scalars()
}
}
// Field (destination) loop ranges
r1, r2 := kernelRanges(size, pbc)
// smallest cell dimension is our typical length scale
L := cellsize[X]
{
if cellsize[Y] < L {
L = cellsize[Y]
}
if cellsize[Z] < L {
L = cellsize[Z]
}
}
progress, progmax := 0, (1+(r2[Y]-r1[Y]))*(1+(r2[Z]-r1[Z])) // progress bar
done := make(chan struct{}, 3) // parallel calculation of one component done?
// Start brute integration
// 9 nested loops, does that stress you out?
// Fortunately, the 5 inner ones usually loop over just one element.
for s := 0; s < 3; s++ { // source index Ksdxyz (parallelized over)
go func(s int) {
u, v, w := s, (s+1)%3, (s+2)%3 // u = direction of source (s), v & w are the orthogonal directions
var (
R, R2 [3]float64 // field and source cell center positions
pole [3]float64 // position of point charge on the surface
points int // counts used integration points
)
for z := r1[Z]; z <= r2[Z]; z++ {
zw := wrap(z, size[Z])
// skip one half, reconstruct from symmetry later
// check on wrapped index instead of loop range so it also works for PBC
if zw > size[Z]/2 {
if s == 0 {
progress += (1 + (r2[Y] - r1[Y]))
}
continue
}
R[Z] = float64(z) * cellsize[Z]
for y := r1[Y]; y <= r2[Y]; y++ {
if s == 0 { // show progress of only one component
progress++
util.Progress(progress, progmax, "Calculating demag kernel")
}
yw := wrap(y, size[Y])
if yw > size[Y]/2 {
continue
}
R[Y] = float64(y) * cellsize[Y]
for x := r1[X]; x <= r2[X]; x++ {
xw := wrap(x, size[X])
if xw > size[X]/2 {
continue
}
R[X] = float64(x) * cellsize[X]
// choose number of integration points depending on how far we are from source.
dx, dy, dz := delta(x)*cellsize[X], delta(y)*cellsize[Y], delta(z)*cellsize[Z]
d := math.Sqrt(dx*dx + dy*dy + dz*dz)
if d == 0 {
d = L
}
maxSize := d / accuracy // maximum acceptable integration size
nv := int(math.Max(cellsize[v]/maxSize, 1) + 0.5)
nw := int(math.Max(cellsize[w]/maxSize, 1) + 0.5)
nx := int(math.Max(cellsize[X]/maxSize, 1) + 0.5)
ny := int(math.Max(cellsize[Y]/maxSize, 1) + 0.5)
nz := int(math.Max(cellsize[Z]/maxSize, 1) + 0.5)
// Stagger source and destination grids.
// Massively improves accuracy, see note.
nv *= 2
nw *= 2
util.Assert(nv > 0 && nw > 0 && nx > 0 && ny > 0 && nz > 0)
scale := 1 / float64(nv*nw*nx*ny*nz)
surface := cellsize[v] * cellsize[w] // the two directions perpendicular to direction s
charge := surface * scale
pu1 := cellsize[u] / 2. // positive pole center
pu2 := -pu1 // negative pole center
// Do surface integral over source cell, accumulate in B
var B [3]float64
for i := 0; i < nv; i++ {
pv := -(cellsize[v] / 2.) + cellsize[v]/float64(2*nv) + float64(i)*(cellsize[v]/float64(nv))
pole[v] = pv
for j := 0; j < nw; j++ {
pw := -(cellsize[w] / 2.) + cellsize[w]/float64(2*nw) + float64(j)*(cellsize[w]/float64(nw))
pole[w] = pw
// Do volume integral over destination cell
for α := 0; α < nx; α++ {
rx := R[X] - cellsize[X]/2 + cellsize[X]/float64(2*nx) + (cellsize[X]/float64(nx))*float64(α)
for β := 0; β < ny; β++ {
ry := R[Y] - cellsize[Y]/2 + cellsize[Y]/float64(2*ny) + (cellsize[Y]/float64(ny))*float64(β)
for γ := 0; γ < nz; γ++ {
rz := R[Z] - cellsize[Z]/2 + cellsize[Z]/float64(2*nz) + (cellsize[Z]/float64(nz))*float64(γ)
points++
pole[u] = pu1
R2[X], R2[Y], R2[Z] = rx-pole[X], ry-pole[Y], rz-pole[Z]
r := math.Sqrt(R2[X]*R2[X] + R2[Y]*R2[Y] + R2[Z]*R2[Z])
qr := charge / (4 * math.Pi * r * r * r)
bx := R2[X] * qr
by := R2[Y] * qr
bz := R2[Z] * qr
pole[u] = pu2
R2[X], R2[Y], R2[Z] = rx-pole[X], ry-pole[Y], rz-pole[Z]
r = math.Sqrt(R2[X]*R2[X] + R2[Y]*R2[Y] + R2[Z]*R2[Z])
qr = -charge / (4 * math.Pi * r * r * r)
B[X] += (bx + R2[X]*qr) // addition ordered for accuracy
B[Y] += (by + R2[Y]*qr)
B[Z] += (bz + R2[Z]*qr)
}
}
}
}
}
for d := s; d < 3; d++ { // destination index Ksdxyz
array[s][d][zw][yw][xw] += float32(B[d]) // += needed in case of PBC
}
}
}
}
done <- struct{}{} // notify parallel computation of this component is done
}(s)
}
// wait for all 3 components to finish
<-done
<-done
<-done
// Reconstruct skipped parts from symmetry (X)
for z := 0; z < size[Z]; z++ {
for y := 0; y < size[Y]; y++ {
for x := size[X]/2 + 1; x < size[X]; x++ {
x2 := size[X] - x
array[X][X][z][y][x] = array[X][X][z][y][x2]
array[X][Y][z][y][x] = -array[X][Y][z][y][x2]
array[X][Z][z][y][x] = -array[X][Z][z][y][x2]
array[Y][Y][z][y][x] = array[Y][Y][z][y][x2]
array[Y][Z][z][y][x] = array[Y][Z][z][y][x2]
array[Z][Z][z][y][x] = array[Z][Z][z][y][x2]
}
}
}
// Reconstruct skipped parts from symmetry (Y)
for z := 0; z < size[Z]; z++ {
for y := size[Y]/2 + 1; y < size[Y]; y++ {
y2 := size[Y] - y
for x := 0; x < size[X]; x++ {
array[X][X][z][y][x] = array[X][X][z][y2][x]
array[X][Y][z][y][x] = -array[X][Y][z][y2][x]
array[X][Z][z][y][x] = array[X][Z][z][y2][x]
array[Y][Y][z][y][x] = array[Y][Y][z][y2][x]
array[Y][Z][z][y][x] = -array[Y][Z][z][y2][x]
array[Z][Z][z][y][x] = array[Z][Z][z][y2][x]
}
}
}
// Reconstruct skipped parts from symmetry (Z)
for z := size[Z]/2 + 1; z < size[Z]; z++ {
z2 := size[Z] - z
for y := 0; y < size[Y]; y++ {
for x := 0; x < size[X]; x++ {
array[X][X][z][y][x] = array[X][X][z2][y][x]
array[X][Y][z][y][x] = array[X][Y][z2][y][x]
array[X][Z][z][y][x] = -array[X][Z][z2][y][x]
array[Y][Y][z][y][x] = array[Y][Y][z2][y][x]
array[Y][Z][z][y][x] = -array[Y][Z][z2][y][x]
array[Z][Z][z][y][x] = array[Z][Z][z2][y][x]
}
}
}
// for 2D these elements are zero:
if size[Z] == 1 {
kernel[X][Z] = nil
kernel[Y][Z] = nil
}
// make result symmetric for tools that expect it so.
kernel[Y][X] = kernel[X][Y]
kernel[Z][X] = kernel[X][Z]
kernel[Z][Y] = kernel[Y][Z]
return kernel
}
func (geometry *geom) setGeom(s Shape) {
SetBusy(true)
defer SetBusy(false)
if s == nil {
// TODO: would be nice not to save volume if entirely filled
s = universe
}
geometry.shape = s
if geometry.Gpu().IsNil() {
geometry.buffer = cuda.NewSlice(1, geometry.Mesh().Size())
}
host := data.NewSlice(1, geometry.Gpu().Size())
array := host.Scalars()
V := host
v := array
n := geometry.Mesh().Size()
c := geometry.Mesh().CellSize()
cx, cy, cz := c[X], c[Y], c[Z]
progress, progmax := 0, n[Y]*n[Z]
var ok bool
for iz := 0; iz < n[Z]; iz++ {
for iy := 0; iy < n[Y]; iy++ {
progress++
util.Progress(progress, progmax, "Initializing geometry")
for ix := 0; ix < n[X]; ix++ {
r := Index2Coord(ix, iy, iz)
x0, y0, z0 := r[X], r[Y], r[Z]
// check if center and all vertices lie inside or all outside
allIn, allOut := true, true
if s(x0, y0, z0) {
allOut = false
} else {
allIn = false
}
if edgeSmooth != 0 { // center is sufficient if we're not really smoothing
for _, Δx := range []float64{-cx / 2, cx / 2} {
for _, Δy := range []float64{-cy / 2, cy / 2} {
for _, Δz := range []float64{-cz / 2, cz / 2} {
if s(x0+Δx, y0+Δy, z0+Δz) { // inside
allOut = false
} else {
allIn = false
}
}
}
}
}
switch {
case allIn:
v[iz][iy][ix] = 1
ok = true
case allOut:
v[iz][iy][ix] = 0
default:
v[iz][iy][ix] = geometry.cellVolume(ix, iy, iz)
ok = ok || (v[iz][iy][ix] != 0)
}
}
}
}
if !ok {
util.Fatal("SetGeom: geometry completely empty")
}
data.Copy(geometry.buffer, V)
// M inside geom but previously outside needs to be re-inited
needupload := false
geomlist := host.Host()[0]
mhost := M.Buffer().HostCopy()
m := mhost.Host()
rng := rand.New(rand.NewSource(0))
for i := range m[0] {
if geomlist[i] != 0 {
mx, my, mz := m[X][i], m[Y][i], m[Z][i]
if mx == 0 && my == 0 && mz == 0 {
needupload = true
rnd := randomDir(rng)
m[X][i], m[Y][i], m[Z][i] = float32(rnd[X]), float32(rnd[Y]), float32(rnd[Z])
}
}
}
if needupload {
data.Copy(M.Buffer(), mhost)
}
M.normalize() // removes m outside vol
}
// Kernel for the vertical derivative of the force on an MFM tip due to mx, my, mz.
// This is the 2nd derivative of the energy w.r.t. z.
func MFMKernel(mesh *d.Mesh, lift, tipsize float64) (kernel [3]*d.Slice) {
const TipCharge = 1 / Mu0 // tip charge
const Δ = 1e-9 // tip oscillation, take 2nd derivative over this distance
util.AssertMsg(lift > 0, "MFM tip crashed into sample, please lift the new one higher")
{ // Kernel mesh is 2x larger than input, instead in case of PBC
pbc := mesh.PBC()
sz := padSize(mesh.Size(), pbc)
cs := mesh.CellSize()
mesh = d.NewMesh(sz[X], sz[Y], sz[Z], cs[X], cs[Y], cs[Z], pbc[:]...)
}
// Shorthand
size := mesh.Size()
pbc := mesh.PBC()
cellsize := mesh.CellSize()
volume := cellsize[X] * cellsize[Y] * cellsize[Z]
fmt.Println("calculating MFM kernel")
// Sanity check
{
util.Assert(size[Z] >= 1 && size[Y] >= 2 && size[X] >= 2)
util.Assert(cellsize[X] > 0 && cellsize[Y] > 0 && cellsize[Z] > 0)
util.AssertMsg(size[X]%2 == 0 && size[Y]%2 == 0, "Even kernel size needed")
if size[Z] > 1 {
util.AssertMsg(size[Z]%2 == 0, "Even kernel size needed")
}
}
// Allocate only upper diagonal part. The rest is symmetric due to reciprocity.
var K [3][][][]float32
for i := 0; i < 3; i++ {
kernel[i] = d.NewSlice(1, mesh.Size())
K[i] = kernel[i].Scalars()
}
r1, r2 := kernelRanges(size, pbc)
progress, progmax := 0, (1+r2[Y]-r1[Y])*(1+r2[Z]-r1[Z])
for iz := r1[Z]; iz <= r2[Z]; iz++ {
zw := wrap(iz, size[Z])
z := float64(iz) * cellsize[Z]
for iy := r1[Y]; iy <= r2[Y]; iy++ {
yw := wrap(iy, size[Y])
y := float64(iy) * cellsize[Y]
progress++
util.Progress(progress, progmax, "Calculating MFM kernel")
for ix := r1[X]; ix <= r2[X]; ix++ {
x := float64(ix) * cellsize[X]
xw := wrap(ix, size[X])
for s := 0; s < 3; s++ { // source index Ksxyz
m := d.Vector{0, 0, 0}
m[s] = 1
var E [3]float64 // 3 energies for 2nd derivative
for i := -1; i <= 1; i++ {
I := float64(i)
R := d.Vector{-x, -y, z - (lift + (I * Δ))}
r := R.Len()
B := R.Mul(TipCharge / (4 * math.Pi * r * r * r))
R = d.Vector{-x, -y, z - (lift + tipsize + (I * Δ))}
r = R.Len()
B = B.Add(R.Mul(-TipCharge / (4 * math.Pi * r * r * r)))
E[i+1] = B.Dot(m) * volume // i=-1 stored in E[0]
}
dFdz_tip := ((E[0] - E[1]) + (E[2] - E[1])) / (Δ * Δ) // dFz/dz = d2E/dz2
K[s][zw][yw][xw] += float32(dFdz_tip) // += needed in case of PBC
}
}
}
}
return kernel
}