// ReadMsh reads a mesh for FE analyses
// Note: returns nil on errors
func ReadMsh(dir, fn string) *Mesh {
// new mesh
var o Mesh
// read file
o.FnamePath = filepath.Join(dir, fn)
b, err := io.ReadFile(o.FnamePath)
if LogErr(err, "msh: cannot open mesh file "+o.FnamePath) {
return nil
}
// decode
if LogErr(json.Unmarshal(b, &o), "msh: cannot unmarshal mesh file "+fn+"\n") {
return nil
}
// check
if LogErrCond(len(o.Verts) < 2, "msh: mesh must have at least 2 vertices and 1 cell") {
return nil
}
if LogErrCond(len(o.Cells) < 1, "msh: mesh must have at least 2 vertices and 1 cell") {
return nil
}
// vertex related derived data
o.Ndim = 2
o.Xmin = o.Verts[0].C[0]
o.Ymin = o.Verts[0].C[1]
if len(o.Verts[0].C) > 2 {
o.Zmin = o.Verts[0].C[2]
}
o.Xmax = o.Xmin
o.Ymax = o.Ymin
o.Zmax = o.Zmin
o.VertTag2verts = make(map[int][]*Vert)
for i, v := range o.Verts {
// check vertex id
if LogErrCond(v.Id != i, "msh: vertices must be sequentially numbered. %d != %d\n", v.Id, i) {
return nil
}
// ndim
nd := len(v.C)
if LogErrCond(nd < 2 || nd > 4, "msh: ndim must be 2 or 3\n") {
return nil
}
if nd == 3 {
if math.Abs(v.C[2]) > Ztol {
o.Ndim = 3
}
}
// tags
if v.Tag < 0 {
verts := o.VertTag2verts[v.Tag]
o.VertTag2verts[v.Tag] = append(verts, v)
}
// limits
o.Xmin = min(o.Xmin, v.C[0])
o.Xmax = max(o.Xmax, v.C[0])
o.Ymin = min(o.Ymin, v.C[1])
o.Ymax = max(o.Ymax, v.C[1])
if nd > 2 {
o.Zmin = min(o.Zmin, v.C[2])
o.Zmax = max(o.Zmax, v.C[2])
}
}
// derived data
o.CellTag2cells = make(map[int][]*Cell)
o.FaceTag2cells = make(map[int][]CellFaceId)
o.FaceTag2verts = make(map[int][]int)
o.SeamTag2cells = make(map[int][]CellSeamId)
o.Ctype2cells = make(map[string][]*Cell)
o.Part2cells = make(map[int][]*Cell)
for i, c := range o.Cells {
// check id and tag
if LogErrCond(c.Id != i, "msh: cells must be sequentially numbered. %d != %d\n", c.Id, i) {
return nil
}
if LogErrCond(c.Tag >= 0, "msh: cell tags must be negative\n") {
return nil
}
// face tags
cells := o.CellTag2cells[c.Tag]
o.CellTag2cells[c.Tag] = append(cells, c)
for i, ftag := range c.FTags {
if ftag < 0 {
pairs := o.FaceTag2cells[ftag]
o.FaceTag2cells[ftag] = append(pairs, CellFaceId{c, i})
for _, l := range shp.GetFaceLocalVerts(c.Type, i) {
utl.IntIntsMapAppend(&o.FaceTag2verts, ftag, o.Verts[c.Verts[l]].Id)
}
}
}
// seam tags
if o.Ndim == 3 {
for i, stag := range c.STags {
if stag < 0 {
pairs := o.SeamTag2cells[stag]
o.SeamTag2cells[stag] = append(pairs, CellSeamId{c, i})
}
}
}
// cell type => cells
cells = o.Ctype2cells[c.Type]
o.Ctype2cells[c.Type] = append(cells, c)
// partition => cells
cells = o.Part2cells[c.Part]
o.Part2cells[c.Part] = append(cells, c)
// get shape structure
switch c.Type {
case "joint":
c.IsJoint = true
default:
c.Shp = shp.Get(c.Type)
if LogErrCond(c.Shp == nil, "msh: cannot find shape type == %q\n", c.Type) {
return nil
}
}
}
// remove duplicates
for ftag, verts := range o.FaceTag2verts {
o.FaceTag2verts[ftag] = utl.IntUnique(verts)
}
// log
log.Printf("msh: fn=%s nverts=%d ncells=%d ncelltags=%d nfacetags=%d nseamtags=%d nverttags=%d ncelltypes=%d npart=%d\n", fn, len(o.Verts), len(o.Cells), len(o.CellTag2cells), len(o.FaceTag2cells), len(o.SeamTag2cells), len(o.VertTag2verts), len(o.Ctype2cells), len(o.Part2cells))
return &o
}
// SetStage set nodes, equation numbers and auxiliary data for given stage
func (o *Domain) SetStage(idxstg int, stg *inp.Stage, distr bool) (setstageisok bool) {
// backup state
if idxstg > 0 {
o.create_stage_copy()
if !o.fix_inact_flags(stg.Activate, false) {
return
}
if !o.fix_inact_flags(stg.Deactivate, true) {
}
}
// auxiliary maps for setting boundary conditions
o.FaceConds = make(map[int][]*FaceCond) // cid => conditions
// nodes (active) and elements (active AND in this processor)
o.Nodes = make([]*Node, 0)
o.Elems = make([]Elem, 0)
o.MyCids = make([]int, 0)
// auxiliary maps for dofs and equation types
o.F2Y = make(map[string]string)
o.YandC = GetIsEssenKeyMap()
o.Dof2Tnum = make(map[string]int)
// auxiliary maps for nodes and elements
o.Vid2node = make([]*Node, len(o.Msh.Verts))
o.Cid2elem = make([]Elem, len(o.Msh.Cells))
o.Cid2active = make([]bool, len(o.Msh.Cells))
// subsets of elements
o.ElemConnect = make([]ElemConnector, 0)
o.ElemIntvars = make([]ElemIntvars, 0)
// allocate nodes and cells (active only) -------------------------------------------------------
// for each cell
var eq int // current equation number => total number of equations @ end of loop
o.NnzKb = 0
for _, c := range o.Msh.Cells {
// get element data and information structure
edat := o.Reg.Etag2data(c.Tag)
if LogErrCond(edat == nil, "cannot get element's data with etag=%d", c.Tag) {
return
}
if edat.Inact {
continue
}
o.Cid2active[c.Id] = true
// prepare maps of face conditions
for faceId, faceTag := range c.FTags {
if faceTag < 0 {
faceBc := stg.GetFaceBc(faceTag)
if faceBc != nil {
lverts := shp.GetFaceLocalVerts(c.Type, faceId)
gverts := o.faceLocal2globalVerts(lverts, c)
for j, key := range faceBc.Keys {
fcn := Global.Sim.Functions.Get(faceBc.Funcs[j])
if LogErrCond(fcn == nil, "cannot find function named %q corresponding to face tag %d (@ element %d)", faceBc.Funcs[j], faceTag, c.Id) {
return
}
fcond := &FaceCond{faceId, lverts, gverts, key, fcn, faceBc.Extra}
fconds := o.FaceConds[c.Id]
o.FaceConds[c.Id] = append(fconds, fcond)
}
}
}
}
// get element info (such as DOFs, etc.)
info := GetElemInfo(c.Type, edat.Type, o.FaceConds[c.Id])
if info == nil {
return
}
// for non-joint elements, add new DOFs
if !c.IsJoint {
chk.IntAssert(len(info.Dofs), len(c.Verts))
// store y and f information
for ykey, fkey := range info.Y2F {
o.F2Y[fkey] = ykey
o.YandC[ykey] = true
}
// t1 and t2 equations
for _, ykey := range info.T1vars {
o.Dof2Tnum[ykey] = 1
}
for _, ykey := range info.T2vars {
o.Dof2Tnum[ykey] = 2
}
// loop over nodes of this element
var eNdof int // number of DOFs of this elmeent
for j, v := range c.Verts {
// new or existent node
var nod *Node
if o.Vid2node[v] == nil {
nod = NewNode(o.Msh.Verts[v])
o.Vid2node[v] = nod
o.Nodes = append(o.Nodes, nod)
} else {
nod = o.Vid2node[v]
}
// set DOFs and equation numbers
for _, ukey := range info.Dofs[j] {
eq = nod.AddDofAndEq(ukey, eq)
eNdof += 1
}
}
// number of non-zeros
o.NnzKb += eNdof * eNdof
}
// allocate element
mycell := c.Part == Global.Rank // cell belongs to this processor
if !distr {
mycell = true // not distributed simulation => this processor has all cells
}
if mycell {
// new element
ele := NewElem(edat, c.Id, o.Msh, o.FaceConds[c.Id])
if ele == nil {
return
}
o.Cid2elem[c.Id] = ele
o.Elems = append(o.Elems, ele)
o.MyCids = append(o.MyCids, ele.Id())
// give equation numbers to new element
eqs := make([][]int, len(c.Verts))
for j, v := range c.Verts {
for _, dof := range o.Vid2node[v].Dofs {
eqs[j] = append(eqs[j], dof.Eq)
}
}
if LogErrCond(!ele.SetEqs(eqs, nil), "cannot set element equations") {
return
}
// subsets of elements
o.add_element_to_subsets(ele)
}
}
// connect elements (e.g. Joints)
for _, e := range o.ElemConnect {
nnz, ok := e.Connect(o.Cid2elem, o.Msh.Cells[e.Id()])
if LogErrCond(!ok, "Connect failed") {
return
}
o.NnzKb += nnz
}
// logging
log.Printf("dom: stage # %d %s\n", idxstg, stg.Desc)
log.Printf("dom: nnodes=%d nelems=%d\n", len(o.Nodes), len(o.Elems))
// element conditions, essential and natural boundary conditions --------------------------------
// (re)set constraints and prescribed forces structures
o.EssenBcs.Reset()
o.PtNatBcs.Reset()
// element conditions
for _, ec := range stg.EleConds {
cells, ok := o.Msh.CellTag2cells[ec.Tag]
if LogErrCond(!ok, "cannot find cells with tag = %d to assign conditions", ec.Tag) {
return
}
for _, c := range cells {
e := o.Cid2elem[c.Id]
if e != nil { // set conditions only for this processor's / active element
for j, key := range ec.Keys {
fcn := Global.Sim.Functions.Get(ec.Funcs[j])
if LogErrCond(fcn == nil, "Functions.Get failed\n") {
return
}
e.SetEleConds(key, fcn, ec.Extra)
}
}
}
}
// face boundary conditions
for cidx, fcs := range o.FaceConds {
c := o.Msh.Cells[cidx]
for _, fc := range fcs {
lverts := fc.LocalVerts
gverts := o.faceLocal2globalVerts(lverts, c)
var enodes []*Node
for _, v := range gverts {
enodes = append(enodes, o.Vid2node[v])
}
if o.YandC[fc.Cond] {
if !o.EssenBcs.Set(fc.Cond, enodes, fc.Func, fc.Extra) {
return
}
}
}
}
// vertex bounday conditions
for _, nc := range stg.NodeBcs {
verts, ok := o.Msh.VertTag2verts[nc.Tag]
if LogErrCond(!ok, "cannot find vertices with tag = %d to assign node boundary conditions", nc.Tag) {
return
}
for _, v := range verts {
if o.Vid2node[v.Id] != nil { // set BCs only for active nodes
n := o.Vid2node[v.Id]
for j, key := range nc.Keys {
fcn := Global.Sim.Functions.Get(nc.Funcs[j])
if LogErrCond(fcn == nil, "Functions.Get failed\n") {
return
}
if o.YandC[key] {
o.EssenBcs.Set(key, []*Node{n}, fcn, nc.Extra)
} else {
o.PtNatBcs.Set(o.F2Y[key], n, fcn, nc.Extra)
}
}
}
}
}
// resize slices --------------------------------------------------------------------------------
// t1 and t2 equations
o.T1eqs = make([]int, 0)
o.T2eqs = make([]int, 0)
for _, nod := range o.Nodes {
for _, dof := range nod.Dofs {
switch o.Dof2Tnum[dof.Key] {
case 1:
o.T1eqs = append(o.T1eqs, dof.Eq)
case 2:
o.T2eqs = append(o.T2eqs, dof.Eq)
default:
LogErrCond(true, "t1 and t2 equations are incorrectly set")
return
}
}
}
// size of arrays
o.Ny = eq
o.Nlam, o.NnzA = o.EssenBcs.Build(o.Ny)
o.Nyb = o.Ny + o.Nlam
// solution structure and linear solver
o.Sol = new(Solution)
o.Kb = new(la.Triplet)
o.Fb = make([]float64, o.Nyb)
o.Wb = make([]float64, o.Nyb)
o.Kb.Init(o.Nyb, o.Nyb, o.NnzKb+2*o.NnzA)
o.InitLSol = true // tell solver that lis has to be initialised before use
// allocate arrays
o.Sol.Y = make([]float64, o.Ny)
o.Sol.ΔY = make([]float64, o.Ny)
o.Sol.L = make([]float64, o.Nlam)
if !Global.Sim.Data.Steady {
o.Sol.Dydt = make([]float64, o.Ny)
o.Sol.D2ydt2 = make([]float64, o.Ny)
o.Sol.Psi = make([]float64, o.Ny)
o.Sol.Zet = make([]float64, o.Ny)
o.Sol.Chi = make([]float64, o.Ny)
}
// initialise internal variables
if stg.HydroSt {
if !o.SetHydroSt(stg) {
return
}
} else if stg.GeoSt != nil {
if !o.SetGeoSt(stg) {
return
}
} else if stg.IniStress != nil {
if !o.SetIniStress(stg) {
return
}
} else {
for _, e := range o.ElemIntvars {
e.SetIniIvs(o.Sol, nil)
}
}
// import results from another set of files
if stg.Import != nil {
sum := ReadSum(stg.Import.Dir, stg.Import.Fnk)
if LogErrCond(sum == nil, "cannot import state from %s/%s.sim", stg.Import.Dir, stg.Import.Fnk) {
return
}
if !o.In(sum, len(sum.OutTimes)-1, false) {
return
}
if LogErrCond(o.Ny != len(o.Sol.Y), "import failed: length of primary variables vector imported is not equal to the one allocated. make sure the number of DOFs of the imported simulation matches this one. %d != %d", o.Ny, len(o.Sol.Y)) {
return
}
if stg.Import.ResetU {
for _, ele := range o.ElemIntvars {
if LogErrCond(!ele.Ureset(o.Sol), "cannot run reset function of element after displacements are zeroed") {
return
}
}
for _, nod := range o.Nodes {
for _, ukey := range []string{"ux", "uy", "uz"} {
eq := nod.GetEq(ukey)
if eq >= 0 {
o.Sol.Y[eq] = 0
if len(o.Sol.Dydt) > 0 {
o.Sol.Dydt[eq] = 0
o.Sol.D2ydt2[eq] = 0
}
}
}
}
}
}
// logging
if Global.LogBcs {
log.Printf("dom: essential boundary conditions:%v", o.EssenBcs.List(stg.Control.Tf))
log.Printf("dom: ptnatbcs=%v", o.PtNatBcs.List(stg.Control.Tf))
}
log.Printf("dom: ny=%d nlam=%d nnzKb=%d nnzA=%d nt1eqs=%d nt2eqs=%d", o.Ny, o.Nlam, o.NnzKb, o.NnzA, len(o.T1eqs), len(o.T2eqs))
// success
return true
}
// NodesOnPlane finds vertices located on {x,y,z} plane and returns an iterator
// that can be used to extract results on the plane. An {u,v}-coordinates system is built
// on the plane.
// Input:
// ftag -- cells' face tag; e.g. -31
// Output:
// dat -- plane data holding vertices on plane and other information; see above
// Note:
// 1) this function works with 3D cells only
// 2) faces on cells must be either "qua4" or "qua8" types
// 3) middle nodes in "qua8" are disregarded in order to buidl an {u,v} grid
// 4) the resulting mesh on plane must be equally spaced; i.e. Δx and Δy are constant;
// but not necessarily equal to each other
func NodesOnPlane(ftag int) *PlaneData {
// check
ndim := Dom.Msh.Ndim
if ndim != 3 {
chk.Panic("this function works in 3D only")
}
// loop over cells on face with given face tag
var dat PlaneData
dat.Plane = -1
dat.Ids = make(map[int]bool)
dat.Dx = make([]float64, ndim)
Δx := make([]float64, ndim)
first := true
cells := Dom.Msh.FaceTag2cells[ftag]
for _, cell := range cells {
ctype := cell.C.Type
for fidx, cftag := range cell.C.FTags {
if cftag == ftag {
// check face type
ftype := shp.GetFaceType(ctype)
if !(ftype == "qua4" || ftype == "qua8") {
chk.Panic("can only handle qua4 or qua8 faces for now. ftype=%q", ftype)
}
// vertices on face
flvids := shp.GetFaceLocalVerts(ctype, fidx)
nv := len(flvids)
if nv == 8 {
nv = 4 // avoid middle nodes
}
for i := 0; i < nv; i++ {
vid := cell.C.Verts[flvids[i]]
dat.Ids[vid] = true
}
// compute and check increments in global coordinates
for i := 1; i < nv; i++ {
a := cell.C.Verts[flvids[i]]
b := cell.C.Verts[flvids[i-1]]
xa := Dom.Msh.Verts[a].C
xb := Dom.Msh.Verts[b].C
for j := 0; j < ndim; j++ {
Δx[j] = max(Δx[j], math.Abs(xa[j]-xb[j]))
}
}
if first {
for j := 0; j < ndim; j++ {
dat.Dx[j] = Δx[j]
}
first = false
} else {
for j := 0; j < ndim; j++ {
if math.Abs(dat.Dx[j]-Δx[j]) > 1e-10 {
chk.Panic("all faces must have the same Δx,Δy,Δz")
}
}
}
// find which plane vertices are located on => which plane this face is parallel to
perpto := -1 // "perpendicular to" indicator
switch {
case Δx[0] < DIST_TOL: // plane perpendicular to x-axis
perpto = 0
case Δx[1] < DIST_TOL: // plane perpendicular to y-axis
perpto = 1
case Δx[2] < DIST_TOL: // plane perpendicular to z-axis
perpto = 2
default:
chk.Panic("planes must be perpendicular to one of the x-y-z axes")
}
if dat.Plane < 0 {
dat.Plane = perpto
} else {
if perpto != dat.Plane {
chk.Panic("all planes must be perperdicular to the same axis")
}
}
}
}
}
// uv: indices and increments
dat.Iu = make([]int, 2)
dat.Du = make([]float64, 2)
switch dat.Plane {
case 0: // plane perpendicular to x-axis
dat.Iu = []int{1, 2}
case 1: // plane perpendicular to y-axis
dat.Iu = []int{0, 2}
case 2: // plane perpendicular to z-axis
dat.Iu = []int{0, 1}
}
for j := 0; j < 2; j++ {
dat.Du[j] = dat.Dx[dat.Iu[j]]
}
// uv: limits
dat.Umin = make([]float64, 2)
dat.Umax = make([]float64, 2)
first = true
for vid, _ := range dat.Ids {
x := Dom.Msh.Verts[vid].C
if first {
for j := 0; j < 2; j++ {
dat.Umin[j] = x[dat.Iu[j]]
dat.Umax[j] = x[dat.Iu[j]]
}
first = false
} else {
for j := 0; j < 2; j++ {
dat.Umin[j] = min(dat.Umin[j], x[dat.Iu[j]])
dat.Umax[j] = max(dat.Umax[j], x[dat.Iu[j]])
}
}
}
// uv: size of grid
dat.Nu = make([]int, 2)
for j := 0; j < 2; j++ {
dat.Nu[j] = int((dat.Umax[j]-dat.Umin[j])/dat.Du[j]) + 1
}
// uv: bins
dd := DIST_TOL * 2
nb := 20
dat.Ubins.Init([]float64{dat.Umin[0] - dd, dat.Umin[1] - dd}, []float64{dat.Umax[0] + dd, dat.Umax[1] + dd}, nb)
u := []float64{0, 0}
for vid, _ := range dat.Ids {
x := Dom.Msh.Verts[vid].C
for j := 0; j < 2; j++ {
u[j] = x[dat.Iu[j]]
}
err := dat.Ubins.Append(u, vid)
if err != nil {
chk.Panic("cannot append {u,v} coordinate to bins. u=%v", u)
}
}
// allocate F
dat.F = la.MatAlloc(dat.Nu[0], dat.Nu[1])
return &dat
}