The course is given within NGSSC, the National Graduate School of Scientific Computing.

Detailed schedule for Modules 1-3, given at Uppsala University

Modules 4 and 5 are organized by HPC2N and the Department of Computing Science at Umeå University, and are given in the MIT (Mathematics and Information Technology) building, denoted V on the campus map.

Note that your home department is expected to provide advance payment for travel and housing. After the course has been completed, the costs will be reimbursed from NGSSC by a lump grant of SEK 12 000.

Review material for Week 3's self study

The most important prerequisite in order to be able to digest the material covered in Modules 4 and 5 is a good working knowledge in multidimensional calculus. Any standard text book on the subject covers what is needed, but the recommended one is Gilbert Strang's 1991 text book Calculus, since it is freely available for download.

Sections 13.1-13.7 covers the basic material needed for the Optimization module. For the Finite Element module, also Sections 15.4-15-5 are needed. Read all these sections carefully. Read also earlier parts of the book as needed, if you need to catch up on more material in order to understand the above mentioned sections. Also answer all the "read-through questions" given at the end of each of the above sections. If you then feel comfortable with the material, you can stop there. If you feel you need more training, then do at least the three first odd-numbered exercises (1, 3, 5) in the "problematic" sections. (Choose the odd-numbered exercises since there are answers to these in a downloadable document at the above url.)

Schedule, Modules 4 and 5

Module IV: The Finite Element Method (FEM)
Date	Content	Time	Location
Feb 4	Why FEM? Application examples, short history. Software demonstration example. Mathematical background: vector calculus, integration by parts, inner products, norms, the Cauchy-Schwarz and Poincar\'e inequalities. FEM for an elliptic model problem: derivation, handling of boundary condition.	9:15-12:00	MA146
	Computer lab	13:15-17:00	I'll tell you
Feb 5	FEM for an elliptic model problem (cont.). Properties of the discrete problem, stability, error analysis. Elements in 2D and 3D. Implementation aspects. Mesh generation.	9:15-12:00	MA206
	Computer lab	13:15-17:00
Feb 6	Orientation about FEM for linear elasticity and for incompressible flow.	9:15-12:00	MA226
	Computer lab	13:15-17:00

Module V: Optimization
Date	Content	Time	Location
Feb 7	Introduction, optimization examples. Unconstrained nonlinear optimization. Convergence rate. Multivariate Taylor series. Optimality conditions. Quadratic functions, Newton's method. Problems with basic Newton. Line search. Steepest-descent and Quasi-Newton. Non-linear least-squares.	9:15-12:00	MA136
	Computer lab	13:15-17:00
Feb 8	Optimization with constraints. Special cases: linear programming, quadratic programming. Orientation about numerical methods: penalty and barrier methods, sequential quadratic programming.	9:15-12:00	MA313
	Computer lab	13:15-17:00

For Thursday's computer lab, you need the m-files temperatures.m and param.m

Recommended books

The lecture and the exercises are not based on any particular book. However, acquiring a good book in the subject is highly recommended, since it provides an alternative viewpoint and much more details than we will be able to cover in this short course.

Finite element books:

Mark S. Gockenbach. Understanding and Implementing the Finite Element Method , SIAM, 2006. (Contains material on implementation aspects and solvers.)

Claes Johnson. Numerical solution of partial differential equations by the finite element method , Studentlitteratur, 1987. (Covers equations from a wide range of applications, not only elliptic model problems.)

Optimization books:

Stephen G. Nash, Ariela Sofer. Linear and Nonlinear Programming . Mc-Graw Hill, 1996. (Separate treatment of linear and nonlinear optimization.)

Jorge Nocedal, Stephen J. Wright. Numerical Optimization . Springer, 1999. (A unified treatment of linear and nonlinear optimization on a slightly more advanced level.)

Accommodation

Note that you need to contact the hotel and make the room reservations yourself! Make the reservations as soon as possible, as Umeå is a busy town for various events requiring hotel rooms!

There are several alternatives for accommodation in Umeå. The closest is Hotel Björken, located nearby (300m) the MIT-building. Hotel Björken also acts as a patient hotel serving visitors to the University hospital. The following price information is for 2007 and may change 2008.

Price per night (Sun, Mon, Tue, Wed, Thu)
Single room 950	Double room 1235
Weekend price per night (Fri, Sat)
Single room 590	Double room 790
Address:
Lasarettsbacken 10 SE-907 19 Umeå, Sweden
Phone number:
+46(0)90-108700

Transportation to Umeå

The most convenient way to travel to Umeå (UME) is by air via Stockholm Arlanda International Airport (ARN) or Stockholm Bromma Airport (BMA). Three airlines service Umeå: Fly Nordic (from ARN), Scandinavian Airlines (from ARN), and Malmö Aviation (from BMA). Book early for the cheapest tickets! It is also possible to go by night train from Stockholm to Umeå (> 10 h).

The airport is located 4 kilometers from downtown Umeå. A bus service from Umeå Airport to the University and Umeå downtown is available for all flights. Taxi fare from the airport to Hotel Björken is approximately SEK 140. Ask for a unit price for the travel from Umeå airport to your hotel. For air airport bus information and timetables for other bus services, see Umeå Lokaltrafik (ULTRA).

Interactive map over Umeå. (Only in Swedish.)