Пример #1
0
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
}
Пример #2
0
// 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
}
Пример #3
0
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
}
Пример #4
0
// 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
}