damped_newton(3rheolef)

💅 damped_newton — the nonlinear solver glow-up

okay bestie, welcome to damped_newton(3rheolef), part of the rheolef-7.2 era 🎀 this is the nonlinear solver that just gets you.

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✨ NAME ✨

damped_newton — nonlinear solver (rheolef-7.2) 🦋

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🌸 SYNOPSIS 🌸

template <class Problem, class Field, class Real, class Size>
int damped_newton (const Problem& F, Field& u, Real& tol, Size& max_iter, odiststream* p_derr=0)

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👑 DESCRIPTION 👑

so this function is giving generic damped Newton method, and what it does is solve this little problem right here:

F(u) = 0

now real talk: the damped Newton method is more robust than the basic Newton one — like, it converges from any initial value. no cap. that's just built different. 🔥

a simple call to the algorithm looks like this:

my_problem P;
field uh (Xh);
damped_newton (P, uh, tol, max_iter);

okay but here's the tea ☕ — on top of all the members you already need for the newton(3) method, the damped variant asks for two extra members:

class my_problem {
public:
  ...
  value_type derivative_trans_mult (const value_type& mrh) const;
  Float space_norm (const value_type& uh) const;
};

so what are these two doing?

• derivative_trans_mult — this one is used for computing the damping coefficient 💅
• space_norm — this usually represents an L2 norm, and formally it's like:

                    /
space_norm(uh) = sqrt |       |uh(x)|^2 dx
                    / Omega

she's giving math, she's giving norm energy, she ate 🍓

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🧚 EXAMPLE 🧚

go look at the p_laplacian_damped_newton.cc example and the usersguide for more. iykyk ✨

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💀 IMPLEMENTATION 💀

this documentation has been generated from file main/lib/damped_newton.h — that's where she lives, that's her home 🏠

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🫶 AUTHOR 🫶

Pierre Saramito <Pierre.Saramito@imag.fr> — the icon, the legend, the moment 👑

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🌈 COPYRIGHT 🌈

Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>.

This is free software: you are free to change and redistribute it. There is NO WARRANTY, to the extent permitted by law. ⚠️ (yes that's the all-caps serious part, respect it bestie)

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rheolef, Version 7.2 — that's the source and version energy, and the date vibe is straight from the damped_newton(3rheolef) footer era. mwah 💋 go solve something nonlinear, you got this 💖