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make gmres more robust for singular operators #153

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Merged
Jutho merged 1 commit into from
May 7, 2026
Merged

make gmres more robust for singular operators #153

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31 changes: 22 additions & 9 deletions src/linsolve/gmres.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -52,7 +52,7 @@ function linsolve(operator, b, x₀, alg::GMRES, a₀::Number = 0, a₁::Number
lmul!(gs[1], y)
β = convert(S, abs(y[2]))

while (β > tol && length(fact) < krylovdim) # inner arnoldi loop
while (!iszero(R[k, k]) && β > tol && length(fact) < krylovdim) # inner arnoldi loop
if alg.verbosity >= EACHITERATION_LEVEL
@info "GMRES linsolve in iteration $numiter; step $k: normres = $(normres2string(β))"
end
Expand All @@ -69,32 +69,45 @@ function linsolve(operator, b, x₀, alg::GMRES, a₀::Number = 0, a₁::Number
R[k, k] = α₀ + α₁ * H[k, k]
end

# Apply Givens rotations
# Apply old Givens rotations
Rk = view(R, :, k)
@inbounds for i in 1:(k - 1)
lmul!(gs[i], Rk)
end
gs[k], R[k, k] = givens(R[k, k], α₁ * normres(fact), k, k + 1)

# Apply Givens rotations to right hand side
y[k + 1] = zero(T)
lmul!(gs[k], y)
# Compute new Givens rotations for final row and also apply to right hand side
if hypot(R[k, k], α₁ * normres(fact)) < tol
if alg.verbosity >= WARN_LEVEL
@warn "GMRES linsolve in iteration $numiter; step $k: linear operator is singular in Krylov subspace"
end
# rotate all the weight into y[k + 1]
gs[k], y[k + 1] = givens(zero(T), y[k], k + 1, k)
y[k] = zero(T)
R[k, k] = zero(T)
else
gs[k], R[k, k] = givens(R[k, k], α₁ * normres(fact), k, k + 1)
y[k + 1] = zero(T)
lmul!(gs[k], y)
end

# New error
β = convert(S, abs(y[k + 1]))
end

# Solve upper triangular system
y2 = copy(y)
ldiv!(UpperTriangular(R), y, 1:k)
if iszero(R[k, k]) && iszero(y[k])
ldiv!(UpperTriangular(R), y, 1:(k - 1))
else
ldiv!(UpperTriangular(R), y, 1:k)
end

# Update x
V = basis(fact)
@inbounds for i in 1:k
x = add!!(x, V[i], y[i])
end

if β > tol
if β > tol && numiter < maxiter
# Recompute residual without reevaluating operator
w = residual(fact)
push!(V, scale!!(w, 1 / normres(fact)))
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