fix: run PETSc with QR

Author: avik-pal

benchmarks/NonlinearProblem/nonlinear_battery_problem.jmd

@@ -58,7 +58,9 @@ solvers_all = [
     (; pkg = :nonlinearsolve,       name = "Levenberg-Marquardt (No Geodesic Accln.)",               solver = Dict(:alg => LevenbergMarquardt(; disable_geodesic = Val(true)))),
     (; pkg = :nonlinearsolve,       name = "Levenberg-Marquardt (No Geodesic Accln.) with Cholesky", solver = Dict(:alg => LevenbergMarquardt(; disable_geodesic = Val(true), linsolve = CholeskyFactorization()))),
     (; pkg = :wrapper,              name = "Newton Raphson [PETSc]",                                 solver = Dict(:alg => PETScSNES(; snes_type = "newtonls", snes_linesearch_type = "basic"))),
+    (; pkg = :wrapper,              name = "Newton Raphson with QR [PETSc]",                         solver = Dict(:alg => PETScSNES(; snes_type = "newtonls", snes_linesearch_type = "basic", pc_type = "qr"))),
     (; pkg = :wrapper,              name = "Newton Raphson with BackTracking [PETSc]",               solver = Dict(:alg => PETScSNES(; snes_type = "newtonls"))),
+    (; pkg = :wrapper,              name = "Newton Raphson with BackTracking & QR [PETSc]",          solver = Dict(:alg => PETScSNES(; snes_type = "newtonls", pc_type = "qr"))),
     (; pkg = :wrapper,              name = "Trust Region [PETSc]",                                   solver = Dict(:alg => PETScSNES(; snes_type = "newtontr"))),
     (; pkg = :wrapper,              name = "Newton Krylov with GMRES [PETSc]",                       solver = Dict(:alg => PETScSNES(; snes_type = "newtonls", snes_linesearch_type = "basic", ksp_type = "gmres"))),
     (; pkg = :wrapper,              name = "Modified Powell [MINPACK]",                              solver = Dict(:alg => CMINPACK(; method = :hybr))),