From 0610e6c96b4a8df56a9e78285533f856acf89b13 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Fri, 26 Feb 2021 17:10:54 -0700 Subject: [PATCH] Make sure we live what we preach. --- doc/doxygen/references.bib | 23 +++++++++++++++++++++++ examples/step-15/doc/results.dox | 16 ++++++++++++++-- 2 files changed, 37 insertions(+), 2 deletions(-) diff --git a/doc/doxygen/references.bib b/doc/doxygen/references.bib index 2694ad09b9..a2f213525e 100644 --- a/doc/doxygen/references.bib +++ b/doc/doxygen/references.bib @@ -251,6 +251,29 @@ } +%------------------------------------------------------------------------------- +% Step 15 +%------------------------------------------------------------------------------- + + + +@Book{GNS08, + author = {I. Griva and S. G. Nash and A. Sofer}, + title = {Linear and nonlinear optimization}, + publisher = {SIAM}, + year = 2008, + edition = {2nd}} + +@Book{NW99, + author = {J. Nocedal and S. J. Wright}, + title = {Numerical Optimization}, + publisher = {Springer, New York}, + year = 1999, + series = {Springer Series in Operations Research} +} + + + %------------------------------------------------------------------------------- % Step 18 %------------------------------------------------------------------------------- diff --git a/examples/step-15/doc/results.dox b/examples/step-15/doc/results.dox index 9aa5f0c173..ede6537f2e 100644 --- a/examples/step-15/doc/results.dox +++ b/examples/step-15/doc/results.dox @@ -93,7 +93,7 @@ We will discuss them in the following.

Step length control

Newton's method has two well known properties: -- It does not converge from arbitrarily chosen starting points. Rather, a +- It may not converge from arbitrarily chosen starting points. Rather, a starting point has to be close enough to the solution to guarantee convergence. However, we can enlarge the area from which Newton's method converges by damping the iteration using a step length 0<$\alpha^n\le @@ -147,7 +147,19 @@ engineering accuracy — substantially fewer than we need with the current version of the program. More details on globalization methods including backtracking can be found, -for example, in Griva, Nash, Sofer: Linear and nonlinear optimization (2009). +for example, in @cite GNS08 and @cite NW99. + +A separate point, very much worthwhile making, however, is that in practice +the implementation of efficient nonlinear solvers is about as complicated as +the implementation of efficient finite element methods. One should not +attempt to reinvent the wheel by implementing all of the necessary steps +oneself. Rather, just like building finite element solvers on libraries +such as deal.II, one should be building nonlinear solvers on libraries such +as [SUNDIALS](https://computing.llnl.gov/projects/sundials). In fact, +deal.II has interfaces to SUNDIALS and in particular to its nonlinear solver +sub-package KINSOL through the SUNDIALS::KINSOL class. It would not be +very difficult to base the current problem on that interface. +

Integrating mesh refinement and nonlinear and linear solvers

-- 2.39.5