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Add Assignment 1 stuff. Formulas from textbook

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Isaac Shoebottom 2025-01-29 17:27:17 -04:00
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Assignment/1/HW1.pdf Normal file
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Assignment/1/eikonal.jl Normal file
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using DelimitedFiles
# Solves the Eikonal equation using the Fast Sweeping Method
# Input is in file with name stored in source
# Input domain has ni x nj values, with a spacing of h
# Default tolerance is 1E-6
# Returns ni x nj solution matrix without extra layer of points
function solveEikonal(ni, nj, h, source, tol = 1E-6)
F = zeros(ni+2, nj+2)
U = ones(ni+2, nj+2) * Inf
initialize!(F, U, ni, nj, source)
maxerr = 1
while maxerr > tol
maxerr = 0
maxerr = sweep!(U, ni+1, 2, 2, nj+1, F, h, maxerr) # North-East
maxerr = sweep!(U, ni+1, 2, nj+1, 2, F, h, maxerr) # North-West
maxerr = sweep!(U, 2, ni+1, nj+1, 2, F, h, maxerr) # South-West
maxerr = sweep!(U, 2, ni+1, 2, nj+1, F, h, maxerr) # South-East
end
U[2:ni+1, 2:nj+1]
end
# Perform one set of sweeps on matrix U using directions specified in
# i1,ib,ja,jb, and speed function F, and current value of maximum
# absolute error (err = (U[i, j]-Unew)/U[i, j]), where Unew
# is new value of U[i,j] calculated using solveQuadratic()
# h is the spacing between points
# Returns updated value of maxerr
function sweep!(U, ia, ib, ja, jb, F, h, maxerr)
#stepi = sign(ib - ia)
#stepj = sign(jb - ja)
stepi = 0
stepj = 0
if ib < ia
stepi = -1
else
stepi = 1
end
if jb < ja
stepj = -1
else
stepj = 1
end
for i in ia:stepi:ib
for j in ja:stepj:jb
Unew = solveQuadratic(U, i, j, F, h)
if Unew < U[i, j]
err = (U[i, j] - Unew) / U[i, j]
if err > maxerr
maxerr = err
end
U[i, j] = Unew
end
end
end
maxerr
end
# Solve the discretized Eikonal equation at (i,j), given
# speed function F, and spacing between points h
# Returns the new value of U[i,j]
function solveQuadratic(U, i, j, F, h)
if U[i, j] == 0
return 0
end
a = min(U[i-1, j], U[i+1, j])
b = min(U[i, j-1], U[i, j+1])
if abs(a - b) >= h / F[i, j]
return min(a, b) + h / F[i, j]
else
return (a + b + sqrt(2* h^2 / F[i, j]^2 - (a - b)^2)) / 2
end
end
# Reads from source a speed function F defined a ni x nj grid
# as well as coordinates of boundary of front
# (input is terminated with a negative number on last line)
# Also initializes solution matrix U
# U and F are (ni+2) x (nj+2) 2D matrices
# Requires the DelimitedFiles package
function initialize!(F, U, ni, nj, source)
temp = readdlm(source)
for j in 1:nj, i in 1:ni
F[i+1, j+1] = Float64(temp[i, j])
end
for i in ni+1:size(temp, 1)-1 # skip last line that has -1 terminator
# +2: skip border and convert input from 0-based indexing
U[temp[i,1]+2, temp[i,2]+2] = 0
end
# println(U)
# println(F)
nothing
end
# Call on file "ex1.txt" with the following format:
println(solveEikonal(7, 7, 1, "ex1.txt"))
# Call on file "test100.txt" with the following format:
# println(solveEikonal(100, 100, 1, "test100.txt"))

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Assignment/1/ex1.txt Normal file
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1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
3 3
-1

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Assignment/1/test100.txt Normal file
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1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
50 50
-1