diff --git a/Assignment/1/HW1.pdf b/Assignment/1/HW1.pdf new file mode 100644 index 0000000..496713b Binary files /dev/null and b/Assignment/1/HW1.pdf differ diff --git a/Assignment/1/eikonal.jl b/Assignment/1/eikonal.jl new file mode 100644 index 0000000..4ee7854 --- /dev/null +++ b/Assignment/1/eikonal.jl @@ -0,0 +1,99 @@ +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")) \ No newline at end of file diff --git a/Assignment/1/ex1.txt b/Assignment/1/ex1.txt new file mode 100644 index 0000000..7fe914a --- /dev/null +++ b/Assignment/1/ex1.txt @@ -0,0 +1,9 @@ +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 diff --git a/Assignment/1/test100.txt b/Assignment/1/test100.txt new file mode 100644 index 0000000..8684f09 --- /dev/null +++ b/Assignment/1/test100.txt @@ -0,0 +1,102 @@ +1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 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