Algorithms and Bicycles

Pam Frost Gorder, “Multicore Processors for Science and Engineering”, IEEE Computing in Science and Engineering, March/April 2007, pp3–7

A very informal review/introduction to the possible impact of the modern multicore CPUs such as Intel Core 2 Duo and IBM Cell processor. The subject of the paper becomes especially significant in the context of Intel’s demonstration of the 80 core CPU:

http://www.intel.com/research/platform/terascale/teraflops.htm?iid=homepage+80core

I think the development of these processors is going to change the way we look at electromagnetic problems. Currently, when we try to solve an EM problem, we formulate into some integral equation, then discretize it using MoM and then we develop the algorithms to solve it efficiently. I think this must change: I propose that after formulating the integral equation and before discretization, we will have to look at the architecture of the system where it is going to be solved. We will have to tailor our discretization and solution methodologies to match the architecture.

This is a paper worth reading for an overview. Thanks to my colleague and friend, Dr. Andy Mathis for getting me a copy of it.

Ref: Weiping Shi, Jianguo Liu, Naveen Kakani, Tiejun Wu, “A fast hierarchical algorithm for three dimensional capacitance extraction,” IEEE Trans. Computer Aided Design of Integrated Circuits and Systems, vol. 21, No. 3 March 2002
I like this work. Yes, it has severe limitations and the authors make ridiculous claims. Yet, the idea is fairly sound within the context of the target problems. (more…)

Yesterday (11/04), I rode up to Ward. Started from my office around 11:45AM and reached there around 2:15pm. The climb was uneventful (well, for the second time I managed to reach there without a break!), although cold. By the time I reached there, my fingers were numb. It was so nice to hold a warm cup of coffee in my hands and to feel it becoming alive again:)

But the return journey was miserable. Although I was wearing three layers, I was cold.  I was shaking uncontrollably  and at times I could not keep the bike steady. In fact, I had to stop after every mile, sometimes even before that. It was the longest  downhill in my life. Took me more than an hour and a quarter to go down the 17 miles!  I still don’t understand why I felt so cold. Yes, the numbers weren’t bad: 52 miles and 4000+ feet of climbing. But statistics don’t tell everything.

To compensate for yesterday’s misery, I went out today and rode 50miles of rolling hills and flats. Home-Dillon-McCaslin-75th-Lookout-79th-Niwot Rd-95th. 95th-Oxford-CR119-CO119-WCR1-Rinn Rd-WCR7-CR8-US287-Baseline-95th. Just to make sure that I have a real half-century and not an approximate one, I detoured into Louisville. In the end, the numbers were 50.48miles in 3 hours and 23 minutes.

I had to write this before getting warmed up… Yes, warmed up.

We had a serious winter storm yesterday (10/26) that dumped a lot of snow. But the sun had come out in the late afternoon. So this morning when I saw a ‘bright and white’ morning, riding to work became an obviously uninformed obvious choice. (more…)

Ref: Ozgur Ergul and Levent Gurel, “Enhancing the accuracy of the interpolations and anterpolations in MLFMA,” to appear in IEEE Antennas and Wireless Propagation Letters (Abstract and pdf files are available from the journal website at IEEE.org)

I was talking to my two year old nephew, Kannan, the other day. We were discussing some of the most recent developments in the field of fast algorithms in computational electromagnetics. Well, he is not exactly an expert in this field, but as soon as I mentioned this paper to him, he asked “Uncle Sanjay, is it not what Drs. Song and Chew developed over ten years ago and what a lot of people have been using since then? I think it sounds like mommy taking grandma’s recipe for chicken curry and claiming it to be her own.” (more…)

It was a gorgeous autumn day. The weather was supposed to be in the low 80s and nearly clear sky. It would be a criminal waste if I didn’t get on the bike… or so I thought.

So by 10:30AM I was out of the house. The plan was to do about 65-70 miles of ‘plains’ riding. That meant going east. So I went east. (more…)

What a ride! What a ride!

Rick and I started riding around 10:00am from Masonville, CO, a few miles south of Fort Collins. We rode over Horsetooth reservoir. There were three short but very steep hills that made our hearts beat faster than the latest Intel Core-Duo processors! But the reward was that the views of the lake to the west and the town to the east were fantastic. (more…)

Last week, I read the following paper:

Amir Boag and Boris Livshitz, “Adapative Nonuniform-Grid (NG) Algorithm for Fast Capacitance Extraction”, IEEE Trans. Microwave Theory and Techniques, vol 54, No. 9, Sept. 2006, pp3565-3570.

To begin, I like the idea from an academic point of view. The authors’ primary objective is to construct a technique that has the same asymptotic complexity as that of the static FMM (O(n)) but with a smaller proportionality constant. The central idea used in the development is the following: at sufficiently large distance from a set of finite sources, the potential is a smooth function, and therefore can be interpolated to any given precision. That is, given the potential at a set of points, say sampling points, sufficiently far away from the source, one can accurately compute the potential at a new point in the vicinity of the sampling points by interpolating from the known values. This is common knowledge. (more…)

Well, it certainly felt that way until a mile or two after Glen Haven when it became bad, worse and insane, in that order. (more…)

Yes, it is the day. And I celebrated it by riding my bike for 15 minutes this morning. Rock Creek to Coalton Rd to McCaslin Blvd and back on to Rock Creek. Three miles in all.

There is an element of fear now while going downhill. I suppose that is natural.

The last one month of physical inactivity became a blessing in disguise as I rediscoverd my passion for, well, what else, fast numerical algorithms and mathematics. I have read several technical papers, reviewed some areas in math which were becoming a little rusty and so on. I am working on a paper and will be commenting it on the next couple of days under electromagnetics.