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mfmkernel.go
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mfmkernel.go
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package mag
import (
"bufio"
"fmt"
d "github.com/mumax/3/data"
"github.com/mumax/3/oommf"
"github.com/mumax/3/util"
"math"
"os"
)
func MFMKernel(mesh *d.Mesh, lift, tipsize float64, cacheDir string) (kernel [3]*d.Slice) {
// Cache disabled
if cacheDir == "" {
util.Log(`//Not using kernel cache (-cache="")`)
return CalcMFMKernel(mesh, lift, tipsize)
}
// Error-resilient kernel cache: if anything goes wrong, return calculated kernel.
defer func() {
if err := recover(); err != nil {
util.Log("//Unable to use kernel cache:", err)
kernel = CalcMFMKernel(mesh, lift, tipsize)
}
}()
// Try to load kernel
basename := fmt.Sprint(cacheDir, "/", "mumax3MFMkernel_", mesh.Size(), "_", mesh.PBC(), "_", mesh.CellSize(), "_", lift, "_", tipsize, "_")
var errLoad error
for i := 0; i < 3; i++ {
kernel[i], errLoad = LoadKernel(fmt.Sprint(basename, i, ".ovf"))
if errLoad != nil {
break
}
}
if errLoad != nil {
util.Log("//Did not use cached kernel:", errLoad)
} else {
util.Log("//Using cached kernel:", basename)
return kernel
}
// Could not load kernel: calculate it and save
var errSave error
kernel = CalcMFMKernel(mesh, lift, tipsize)
for i := 0; i < 3; i++ {
compName := fmt.Sprint("Nmfm_", i)
info := d.Meta{Time: float64(0.0), Name: compName, Unit: "1", CellSize: mesh.CellSize(), MeshUnit: "m"}
errSave = SaveKernel(fmt.Sprint(basename, i, ".ovf"), kernel[i], info)
if errSave != nil {
break
}
}
if errSave != nil {
util.Log("//Failed to cache kernel:", errSave)
} else {
util.Log("//Cached kernel:", basename)
}
return kernel
}
func LoadMFMKernel(fname string) (kernel *d.Slice, err error) {
kernel, _, err = oommf.ReadFile(fname)
return
}
func SaveMFMKernel(fname string, kernel *d.Slice) error {
f, err := os.OpenFile(fname, os.O_WRONLY|os.O_TRUNC|os.O_CREATE, 0666)
if err != nil {
return err
}
out := bufio.NewWriter(f)
defer out.Flush()
oommf.WriteOVF2(out, kernel, d.Meta{}, "binary 4")
return nil
}
// 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 CalcMFMKernel(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
}