func (u *ΔUpdater) Update() {
qin := u.in.Array()
qout := u.out.Array()
q0 := u.q0.Array()
qinMul := u.in.Multiplier()
qoutMul := u.out.Multiplier()
q0Mul := u.q0.Multiplier()
COMP := u.in.NComp()
pre := make([]float64, COMP)
for ii := 0; ii < COMP; ii++ {
qoutMul[ii] = qinMul[ii]
pre[ii] = -q0Mul[ii] / qinMul[ii] //0?
}
switch COMP {
case 1:
gpu.Madd(qout.Component(0), qin.Component(0), q0.Component(0), pre[0])
case 3:
gpu.VecMadd(qout, qin, q0, pre)
default:
panic(InputErrF("Δ is not implemented for NComp: ", COMP))
}
}
func (u *SumUpdater) addTerms() {
// TODO: optimize for 0,1,2 or more parents
sum := u.sum
parents := u.parents
if sum.IsSpaceDependent() {
for i := range parents {
parent := parents[i]
weight := u.weight[i]
parMul := make([]float64, sum.NComp())
for c := 0; c < sum.NComp(); c++ {
parMul[c] = weight * parent.Multiplier()[c] / sum.Multiplier()[c]
}
switch sum.NComp() {
case 1:
gpu.Madd(sum.array.Component(0), sum.array.Component(0), parent.array.Component(0), parMul[0])
case 3:
gpu.VecMadd(sum.Array(), sum.Array(), parent.Array(), parMul)
default:
panic(InputErr("sum is not implemented for NComp: " + fmt.Sprint(sum.NComp())))
}
}
} else {
for p, parent := range parents {
for c := range sum.multiplier {
sum.multiplier[c] += parent.multiplier[c] * u.weight[p]
}
}
}
}
func (s *HeunSolver) Step() {
e := GetEngine()
equation := e.equation
// First update all inputs
dt := engine.dt.Scalar()
for i := range equation {
Assert(equation[i].kind == EQN_PDE1)
equation[i].input[0].Update()
}
// Then step all outputs
// and invalidate them.
// stage 0
for i := range equation {
y := equation[i].output[0]
dy := equation[i].input[0]
dyMul := dy.multiplier
checkUniform(dyMul)
s.buffer[i] = Pool.Get(y.NComp(), y.Size3D())
s.buffer[i].CopyFromDevice(dy.Array()) // save for later
gpu.Madd(y.Array(), y.Array(), dy.Array(), dt*dyMul[0]) // initial euler step
y.Invalidate()
}
// Advance time
e.time.SetScalar(e.time.Scalar() + dt)
// update inputs again
for i := range equation {
Assert(equation[i].kind == EQN_PDE1)
equation[i].input[0].Update()
}
// stage 1
for i := range equation {
y := equation[i].output[0]
dy := equation[i].input[0]
dyMul := dy.multiplier
h := float64(dt * dyMul[0])
gpu.MAdd2Async(y.Array(), dy.Array(), 0.5*h, s.buffer[i], -0.5*h, y.Array().Stream) // corrected step
y.Array().Sync()
Pool.Recycle(&s.buffer[i])
y.Invalidate()
}
e.step.SetScalar(e.step.Scalar() + 1) // advance time step
}
// sum += parent
func (sum *Quant) Add(parent *Quant) {
invalidated := false
for c := 0; c < sum.NComp(); c++ {
parComp := parent.array.Component(c)
parMul := parent.multiplier[c]
if parMul == 0 {
continue
}
sumMul := sum.multiplier[c]
sumComp := sum.array.Component(c) // does not alloc
gpu.Madd(sumComp, sumComp, parComp, parMul/sumMul) // divide by sum's multiplier!
invalidated = true
}
if invalidated {
sum.Invalidate()
}
}
func (s *BDFAM12) Step() {
e := GetEngine()
t0 := e.time.Scalar()
s.badSteps.SetScalar(0)
s.iterations.SetScalar(0)
equation := e.equation
//~ make sure that errors history is wiped for t0 = 0 s!
if t0 == 0.0 {
for i := range equation {
s.err_list[i].Init()
s.steps_list[i].Init()
}
}
//~ save everything in the begining
e.UpdateEqRHS()
for i := range equation {
y := equation[i].LHS()
dy := equation[i].RHS()
s.y0buffer[i].CopyFromDevice(y.Array()) //~ save for later
s.dy0buffer[i].CopyFromDevice(dy.Array()) //~ save for later
}
const maxTry = 10 //~ undo at most this many bad steps
const headRoom = 0.8
const maxIterErr = 0.1
const maxIter = 5
const alpha_ref = 0.6
try := 0
restrict_step := false
for {
dt := engine.dt.Scalar()
badStep := false
badIterator := false
er := make([]float64, len(equation))
alp := make([]float64, len(equation))
//~ Do zero-order approximation with explicit Euler
for i := range equation {
y := equation[i].LHS()
dy := equation[i].RHS()
dyMul := dy.multiplier
t_step := dt * dyMul[0]
gpu.Madd(y.Array(), s.y0buffer[i], s.dy0buffer[i], t_step)
y.Invalidate()
}
s.iterations.SetScalar(s.iterations.Scalar() + 1)
//~ Do predictor using implicit Euler
e.time.SetScalar(t0 + dt)
e.UpdateEqRHS()
for i := range equation {
s.dybuffer[i].CopyFromDevice(equation[i].RHS().Array())
}
for i := range equation {
er[i] = maxIterErr
}
iter := 0
err := 1.0
α := 0.0
for {
for i := range equation {
y := equation[i].LHS()
dy := equation[i].RHS()
COMP := dy.NComp()
srCOMP := 1.0 / math.Sqrt(float64(COMP))
h := dt * dy.multiplier[0]
gpu.Madd(s.ybuffer[i], s.y0buffer[i], dy.Array(), h)
tErr := 0.0
for p := 0; p < COMP; p++ {
diffy := float64(s.diff[i].MaxDiff(y.Array().Component(p), s.ybuffer[i].Component(p)))
maxy := float64(s.diff[i].MaxAbs(s.ybuffer[i].Component(p)))
tErr += math.Pow(diffy/(s.maxAbsErr[i].Scalar()+maxy*s.maxRelErr[i].Scalar()), 2.0)
}
tErr = srCOMP * math.Sqrt(tErr)
α = tErr / er[i]
alp[i] = α
s.alpha[i] = α
er[i] = tErr
y.Array().CopyFromDevice(s.ybuffer[i])
y.Invalidate()
}
//~ Get the largest error
sort.Float64s(er)
sort.Float64s(alp)
err = er[len(equation)-1]
α = alp[len(equation)-1]
iter = iter + 1
s.iterations.SetScalar(s.iterations.Scalar() + 1)
//~ Check first if the target error is reached
if err <= maxIterErr {
break
}
//~ If not, then check for convergence
if α >= 1.0 || iter > maxIter {
badIterator = true
break
}
e.UpdateEqRHS()
}
//~ If fixed-point iterator cannot converge, then panic
if badIterator && try == (maxTry-1) {
panic(Bug(fmt.Sprintf("The BDF Euler iterator cannot converge! Please increase the maximum number of iterations and re-run!")))
} else if badIterator {
//~ if there is a bad step in iterator then do hard/soft for step correction for fast/slow convergence
h_alpha := 0.5 * dt
if α > alpha_ref {
h_alpha = dt * math.Pow(alpha_ref/α, 0.5)
}
engine.dt.SetScalar(h_alpha)
restrict_step = true
continue
}
//~ Save function value of the comparator
//~ and restore dy as estimated by explicit Euler
for i := range equation {
s.y1buffer[i].CopyFromDevice(equation[i].LHS().Array())
equation[i].RHS().Array().CopyFromDevice(s.dybuffer[i])
}
//~ Apply embedded 2nd order implicit method (trapezoidal)
for i := range equation {
er[i] = maxIterErr
}
iter = 0
err = 1.0
badIterator = false
for {
for i := range equation {
y := equation[i].LHS()
dy := equation[i].RHS()
COMP := dy.NComp()
srCOMP := 1.0 / math.Sqrt(float64(COMP))
h := float64(dt * dy.multiplier[0])
gpu.AddMadd(s.ybuffer[i], s.y0buffer[i], dy.Array(), s.dy0buffer[i], 0.5*h)
tErr := 0.0
for p := 0; p < COMP; p++ {
diffy := float64(s.diff[i].MaxDiff(y.Array().Component(p), s.ybuffer[i].Component(p)))
maxy := float64(s.diff[i].MaxAbs(s.ybuffer[i].Component(p)))
tErr += math.Pow(diffy/(s.maxAbsErr[i].Scalar()+maxy*s.maxRelErr[i].Scalar()), 2.0)
}
tErr = srCOMP * math.Sqrt(tErr)
alp[i] = tErr / er[i]
er[i] = tErr
y.Array().CopyFromDevice(s.ybuffer[i])
y.Invalidate()
}
//~ Get the largest error
sort.Float64s(er)
sort.Float64s(alp)
err = er[len(equation)-1]
α = alp[len(equation)-1]
iter = iter + 1
s.iterations.SetScalar(s.iterations.Scalar() + 1)
//~ Check first if the target error is reached
if err <= maxIterErr {
break
}
//~ If not, then check for convergence
if α >= 1.0 || iter > maxIter {
badIterator = true
break
}
e.UpdateEqRHS()
}
if badIterator && try == (maxTry-1) {
//~ If fixed-point iterator cannot converge, then panic
panic(Bug(fmt.Sprintf("The BDF Trapezoidal iterator cannot converge! Please decrease the error the maximum number of iterations and re-run!")))
} else if badIterator {
//~ if there is a bad step in iterator then do hard/soft for step correction for fast/slow convergence
h_alpha := 0.5 * dt
if α > alpha_ref {
h_alpha = dt * math.Pow(alpha_ref/α, 0.5)
}
engine.dt.SetScalar(h_alpha)
continue
}
for i := range equation {
y := equation[i].LHS()
COMP := y.NComp()
srCOMP := 1.0 / math.Sqrt(float64(COMP))
tErr := 0.0
for p := 0; p < COMP; p++ {
diffy := float64(s.diff[i].MaxDiff(y.Array().Component(p), s.y1buffer[i].Component(p)))
maxy := float64(s.diff[i].MaxAbs(s.y1buffer[i].Component(p)))
tErr += math.Pow(diffy/(s.maxAbsErr[i].Scalar()+maxy*s.maxRelErr[i].Scalar()), 2.0)
}
tErr = srCOMP * math.Sqrt(tErr)
if tErr > 1.0 {
s.badSteps.SetScalar(s.badSteps.Scalar() + 1)
badStep = true
}
s.err[i].SetScalar(tErr)
//~ Estimate step correction
step_corr := math.Pow(headRoom/tErr, 0.5)
h_r := dt * step_corr
new_dt := h_r
//~ if iterator reported convergence problems, then the step correction should be restricted according to the linear prediction of the sweet convergence spot.
if restrict_step {
h_alpha := dt * math.Pow(alpha_ref/s.alpha[i], 0.5)
new_dt = math.Min(h_r, h_alpha)
restrict_step = false
}
//~ User-defined limiter for the new step. Just for stability experiments.
if new_dt < s.minDt.Scalar() {
new_dt = s.minDt.Scalar()
}
if new_dt > s.maxDt.Scalar() {
new_dt = s.maxDt.Scalar()
}
s.newDt[i] = new_dt
//~ Keep the history of 'good' errors
if !badStep {
s.err_list[i].PushFront(tErr)
s.steps_list[i].PushFront(dt)
if s.err_list[i].Len() == 10 {
s.err_list[i].Remove(s.err_list[i].Back())
s.steps_list[i].Remove(s.steps_list[i].Back())
}
}
}
//~ Get the new timestep
sort.Float64s(s.newDt)
nDt := s.newDt[0]
engine.dt.SetScalar(nDt)
if !badStep || nDt == s.minDt.Scalar() {
break
}
if try > maxTry {
panic(Bug(fmt.Sprint("The solver cannot converge after ", maxTry, " badsteps")))
}
try++
}
//~ Advance step
e.step.SetScalar(e.step.Scalar() + 1) // advance time step
}
func (s *BDFEuler) Step() {
e := GetEngine()
equation := e.equation
for i := range equation {
equation[i].input[0].Update()
}
// get dt here to avoid updates later on.
dt := engine.dt.Scalar()
// Advance time and update all inputs
e.time.SetScalar(e.time.Scalar() + dt)
// Then step all outputs (without intermediate updates!)
// and invalidate them.
for i := range equation {
err := 1.0e38
s.iterations.SetScalar(0)
iter := 0
// Do forward Euler step
// Zero order approximation
y := equation[i].output[0]
dy := equation[i].input[0]
dyMul := dy.multiplier
h := dt * dyMul[0]
s.y0buffer[i].CopyFromDevice(y.Array()) // save for later
gpu.Madd(y.Array(), s.y0buffer[i], dy.Array(), h)
y.Invalidate()
equation[i].input[0].Update()
s.iterations.SetScalar(s.iterations.Scalar() + 1)
// Do backward Euler step and solve it
// Do higher order approximation until converges
// Using fixed-point iterator
maxIterErr := s.maxIterErr[i].Scalar()
maxIter := int(s.maxIter[i].Scalar())
for err > maxIterErr {
gpu.Madd(s.ybuffer[i], s.y0buffer[i], dy.Array(), h)
err = float64(s.diff[i].MaxDiff(y.Array(), s.ybuffer[i]))
sum := float64(s.diff[i].MaxSum(y.Array(), s.ybuffer[i]))
if sum > 0.0 {
err = err / sum
}
iter = iter + 1
s.iterations.SetScalar(s.iterations.Scalar() + 1)
y.Array().CopyFromDevice(s.ybuffer[i])
y.Invalidate()
equation[i].input[0].Update()
if iter > maxIter {
panic(Bug(fmt.Sprintf("The BDF iterator cannot converge for %s! Please decrease the time step and re-run!", y.Name())))
}
}
}
// Advance step
e.step.SetScalar(e.step.Scalar() + 1) // advance step
}
// Take one time step
func (s *RK12Solver) Step() {
e := GetEngine()
equation := e.equation
// First update all inputs
for i := range equation {
Assert(equation[i].kind == EQN_PDE1)
equation[i].input[0].Update()
}
// Then step all outputs
// and invalidate them.
// stage 0
t0 := e.time.Scalar()
for i := range equation {
y := equation[i].output[0]
dy := equation[i].input[0]
dyMul := dy.multiplier
checkUniform(dyMul)
s.dybuffer[i].CopyFromDevice(dy.Array()) // save for later
s.y0buffer[i].CopyFromDevice(y.Array()) // save for later
}
const maxTry = 10 // undo at most this many bad steps
const headRoom = 0.8
try := 0
for {
// We need to update timestep if the step has failed
dt := engine.dt.Scalar()
// initial euler step
for i := range equation {
y := equation[i].output[0]
dy := equation[i].input[0]
dyMul := dy.multiplier
if try > 0 { // restore previous initial conditions
y.Array().CopyFromDevice(s.y0buffer[i])
dy.Array().CopyFromDevice(s.dybuffer[i])
}
gpu.Madd(y.Array(), y.Array(), dy.Array(), dt*dyMul[0])
y.Invalidate()
}
// Advance time
e.time.SetScalar(t0 + dt)
// update inputs again
for i := range equation {
equation[i].input[0].Update()
}
// stage 1
badStep := false
minFactor := 2.0
for i := range equation {
y := equation[i].output[0]
dy := equation[i].input[0]
dyMul := dy.multiplier
h := float64(dt * dyMul[0])
gpu.MAdd2Async(y.Array(), dy.Array(), 0.5*h, s.dybuffer[i], -0.5*h, y.Array().Stream) // corrected step
y.Array().Sync()
// error estimate
stepDiff := s.diff[i].MaxDiff(dy.Array(), s.dybuffer[i]) * h
err := float64(stepDiff)
s.err[i].SetScalar(err)
maxErr := s.maxErr[i].Scalar()
if err > maxErr {
s.badSteps.SetScalar(s.badSteps.Scalar() + 1)
badStep = true
}
if (!badStep || try == maxTry-1) && err > s.peakErr[i].Scalar() {
// peak error should be that of good step, unless last trial which will not be undone
s.peakErr[i].SetScalar(err)
}
factor := 0.0
if !badStep {
factor = math.Sqrt(maxErr / err) //maxErr / err
} else {
factor = math.Pow(maxErr/err, 1./3.)
}
factor *= headRoom
// do not increase/cut too much
// TODO: give user the control:
if factor > 1.5 {
factor = 1.5
}
if factor < 0.1 {
factor = 0.1
}
if factor < minFactor {
minFactor = factor
} // take minimum time increase factor of all eqns.
y.Invalidate()
//if badStep{break} // do not waste time on other equations
}
// Set new time step but do not go beyond min/max bounds
newDt := dt * minFactor
if newDt < s.minDt.Scalar() {
newDt = s.minDt.Scalar()
}
if newDt > s.maxDt.Scalar() {
newDt = s.maxDt.Scalar()
}
e.dt.SetScalar(newDt)
if !badStep || newDt == s.minDt.Scalar() {
break
}
if try > maxTry {
panic(Bug(fmt.Sprint("The solver cannot converge after ", maxTry, " badsteps")))
}
try++
} // end try
// advance time step
e.step.SetScalar(e.step.Scalar() + 1)
}
