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PlanarInterpConvergenceTest.f90
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program PlanarInterpConvergence
use NumberKindsModule
use LoggerModule
use PolyMesh2dModule
use ParticlesModule
use EdgesModule
use FacesModule
use STDIntVectorModule
use FieldModule
use TriScatteredInterpModule
use PSEModule
implicit none
type(Logger) :: exeLog
type(PolyMesh2d) :: triMesh
integer(kint), parameter :: meshSeed = TRI_HEX_SEED
integer(kint) :: initNest
integer(kint) :: maxNest
integer(kint) :: amrLimit
real(kreal) :: ampFactor
type(Field) :: scalar
type(Field) :: estGrad, exactGrad, gradError
type(Field) :: est2ndPartials, exact2ndPartials, partialsError
type(Field) :: estLap, exactLap, lapError
type(TriScatteredInterp) :: interp
real(kreal), parameter :: b = 3.0_kreal
real(kreal), parameter :: xc = 0.0_kreal, yc = 0.0_kreal
real(kreal), parameter :: maxAbsLap = 36.0_kreal
type(PSE) :: pseSetup
integer(kint) :: i, j
integer(kint), parameter :: nn = 501
real(kreal), parameter :: dx = 8.0_kreal / real( nn - 1, kreal)
real(kreal), parameter :: xmin = -4.0_kreal
real(kreal), parameter :: xmax = 4.0_kreal
real(kreal), parameter :: ymin = xmin
real(kreal), parameter :: ymax = xmax
real(kreal) :: x(nn), y(nn)
real(kreal) :: interpScalar(nn,nn), exactScalar(nn,nn)
real(kreal) :: interpGradX(nn,nn), interpGradY(nn,nn), exactGradX(nn,nn), exactGradY(nn,nn)
real(kreal) :: interpLap(nn,nn), exactLapUnif(nn,nn)
real(kreal) :: xVecA(3), xVecB(3), maxGradMag
real(kreal) :: estGradError(9), estLapError(9), interpError(9), meshSize(9)
real(kreal) :: testStart, testEnd
character(len=MAX_STRING_LENGTH) :: logstring
!
!----------------
! PROGRAM START
!----------------
!
call New(exeLog, DEBUG_LOGGING_LEVEL)
amrLimit = 0
ampFactor = 3.0_kreal
do initNest = 0, 8
call cpu_time(testStart)
write(logstring,'(A,I3,A)') "test ", initNest+1, ", of 9..."
call LogMessage(exeLog, TRACE_LOGGING_LEVEL,"Interpolation Convergence : ", logString)
!
! build a mesh
!
maxNest = initNest
call New(triMesh, meshSeed, initNest, maxNest, amrLimit, ampFactor)
! define a scalar field on the mesh
call New(scalar, 1, triMesh%particles%N, "gaussScalar", "n/a")
call New(estGrad,2, triMesh%particles%N, "estGradient", "n/a")
call New(exactGrad,2,triMesh%particles%N,"exactGradient","n/a")
call New(gradError,1,triMesh%particles%N, "gradError", "n/a")
call New(est2ndPartials,3,triMesh%particles%N, "estPartials","n/a")
call New(exact2ndPartials,3,triMesh%particles%N,"exactPartials","n/a")
call New(partialsError,3,triMesh%particles%N, "partialsError","n/a")
call New(estLap, 1, triMesh%particles%N, "estLaplacian","n/a")
call New(exactLap,1, triMesh%particles%N,"exactLaplacian", "n/a")
call New(lapError,1, triMesh%particles%N,"lapError","n/a")
do i = 1, triMesh%particles%N
call InsertScalarToField( scalar, Gaussian( [triMesh%particles%x(i), triMesh%particles%y(i)], b) )
call InsertVectorToField(exactGrad, GaussGrad( [triMesh%particles%x(i), triMesh%particles%y(i)], b))
call InsertVectorToField(exact2ndPartials, Gauss2ndDerivs([triMesh%particles%x(i), triMesh%particles%y(i)], b))
call InsertScalarToField(exactLap, GaussLap([triMesh%particles%x(i), triMesh%particles%y(i)],b) )
enddo
!
! set up interpolation, estimate derivatives
!
call New(interp, triMesh)
call generateFaceUVs(interp, triMesh)
call New(pseSetup, triMesh)
call estimatePartialDerivatives( interp, triMesh, scalar, estGrad, est2ndPartials)
! call SetPlanarCoefficients(interp, triMesh, scalar, estGrad, est2ndPartials)
call SetPlanarCoefficients(interp, triMesh, scalar, exactGrad, exact2ndPartials)
!
! calculate derivative error at particles
!
do i = 1, triMesh%particles%N
xVecA = 0.0_kreal
xVecB = 0.0_kreal
xVecA(1:2) = [estGrad%xComp(i), estGrad%yComp(i)]
xVecB(1:2) = GaussGrad( [triMesh%particles%x(i), triMesh%particles%y(i)], b)
call InsertScalarToField( gradError, sqrt(sum( xVecA - xVecB)))
call InsertScalarToField( estLap, est2ndPartials%xComp(i) + est2ndPartials%zComp(i))
call InsertScalarToField( lapError, estLap%scalar(i) - exactLap%scalar(i))
xVecA = [est2ndPartials%xComp(i), est2ndPartials%yComp(i), est2ndPartials%zComp(i)]
xVecB = Gauss2ndDerivs( [triMesh%particles%x(i), triMesh%particles%y(i)], b)
call InsertVectorToField( partialsError, xVecA - xVecB )
enddo
!
! interpolate to uniform mesh
!
do i = 1, nn
x(i) = xmin + dx * (i-1)
y(i) = ymin + dx * (i-1)
enddo
xVecA = 0.0_kreal
do j = 1, nn
do i = 1, nn
exactScalar(i,j) = Gaussian( [x(j), y(i)], b )
xVecA(1:2) = GaussGrad([x(j),y(i)], b)
exactGradX(i,j) = xVecA(1)
exactGradY(i,j) = xVecA(2)
exactLapUnif(i,j) = GaussLap( [x(j), y(i)], b)
interpScalar(i,j) = InterpolateScalar( interp, triMesh, [x(j),y(i)])
xVecA(1:2) = InterpolateGradient( interp, triMesh, [x(j), y(i)])
interpGradX(i,j) = xVecA(1)
interpGradY(i,j) = xVecA(2)
interpLap(i,j) = InterpolateLaplacian(interp, triMesh, [x(j), y(i)])
enddo
enddo
maxGradMag = MaxMagnitude(exactGrad)
meshSize(initNest+1) = MaxEdgeLength(triMesh%edges, triMesh%particles)
estGradError(initNest+1) = maxval(gradError%scalar)/maxGradMag
estLapError(initNest+1) = maxval(abs(lapError%scalar))/maxAbsLap
interpError(initNest+1) = maxval(abs(interpScalar-exactScalar))
write(6,'(4A24)') "dx", "gradErr-particles", "lapErr-particles", "interp error"
write(6,'(4F24.10)') meshSize(initNest+1), estGradError(initNest+1), estLapError(initNest+1), interpError(initNest+1)
!
! reset for next iteration
!
call cpu_time(testEnd)
write(6,'(A,I8,A,F12.2,A)') "nParticles = ", triMesh%particles%N, ": elapsed time = ", testEnd-testStart, " seconds."
call Delete(pseSetup)
call Delete(interp)
call Delete(lapError)
call Delete(exactLap)
call Delete(estLap)
call Delete(partialsError)
call Delete(exact2ndPartials)
call Delete(est2ndPartials)
call Delete(gradError)
call Delete(exactGrad)
call Delete(estGrad)
call Delete(scalar)
call Delete(triMesh)
call LogMessage(exeLog,TRACE_LOGGING_LEVEL, "test complete for initNest = ", initNest)
enddo
write(6,'(4A24)') "dx", "gradErr-particles", "lapErr-particles", "interp error"
do i = 1, 9
write(6,'(4F24.10)') meshSize(i), estGradError(i), estLapError(i), interpError(i)
enddo
contains
function Gaussian( xy, b )
real(kreal) :: Gaussian
real(kreal), intent(in) :: xy(2)
real(kreal), intent(in) :: b
Gaussian = exp( - b * b * ( (xy(1)-xc)*(xy(1)-xc) + (xy(2)-yc)*(xy(2)-yc)))
end function
function GaussGrad(xy, b)
real(kreal) :: GaussGrad(2)
real(kreal), intent(in) :: xy(2)
real(kreal), intent(in) :: b
GaussGrad(1) = xy(1)-xc
GaussGrad(2) = xy(2)-yc
GaussGrad = -2.0_kreal * GaussGrad * b * b * exp( - b * b * ( (xy(1)-xc)*(xy(1)-xc) + (xy(2)-yc)*(xy(2)-yc) ))
end function
function GaussLap(xy, b)
real(kreal) :: GaussLap
real(kreal), intent(in) :: xy(2)
real(kreal), intent(in) :: b
GaussLap = ( b*b * ( (xy(1)-xc)*(xy(1)-xc) + (xy(2)-yc)*(xy(2)-yc) ) - 1.0_kreal ) * 4.0_kreal * b * b * &
exp( - b * b * ( (xy(1)-xc)*(xy(1)-xc) + (xy(2)-yc)*(xy(2)-yc) ))
end function
function Gauss2ndDerivs( xy, b)
real(kreal) :: Gauss2ndDerivs(3)
real(kreal), intent(in) :: xy(2)
real(kreal), intent(in) :: b
Gauss2ndDerivs(1) = 2.0_kreal * b * b *(2.0_kreal * b*b *(xy(1)-xc)*(xy(1)-xc) - 1.0_kreal)
Gauss2ndDerivs(2) = 4.0_kreal * b**4 * (xy(1)-xc)*(xy(2)-yc)
Gauss2ndDerivs(3) = 2.0_kreal * b * b *(2.0_kreal * b*b * (xy(2)-yc)*(xy(2)-yc) - 1.0_kreal)
Gauss2ndDerivs = Gauss2ndDerivs * exp( - b * b * ( (xy(1)-xc)*(xy(1)-xc) + (xy(2)-yc)*(xy(2)-yc) ))
end function
end program