Numerical analysis of the Galerkin and weak Galerkin method for the Helmholtz equation with high wave number

Event date: Wednesday, November 2, 2016
Location: Clements Hall 126
Time: 3:30–4:30pm

Featured Speaker: Dr. Zhimin ZhangDepartment of Mathematics, Wayne State University and the Beijing Center for Computational Science

Abstract: We study convergence property of the weak Galerkin method of fixed degree p and supercovergence property of the linear finite element method for the Helmholtz problem with large wave number.

  1. Using a modified duality argument, we improve the existing error estimates of the WG method, in particular, the error estimates with explicit dependence on the wave number k are derived, it is shown that if k(kh)p+1 is sufficiently small, then the pollution error in the energy norm is bounded by O(k(kh)2p), which coincides with the phase error of the finite element method obtained by existent dispersion analyses.
  2. For linear finite element method under certain mesh condition, we obtain the H1-error estimate with explicit dependence on the wave number k and show that the error between the finite element solution and the linear interpolation of the exact solution is superconvergent in the H1-seminorm, although the pollution error still exists. We proved a similar result for the recovered gradient by polynomial preserving recovery (PPR) and found that the PPR can only improve the interpolation error and has no effect on the pollution error. Furthermore, we estimated the error between the finite element gradient and recovered gradient and discovered that the pollution error is canceled between these two quantities. Finally, we apply the Richardson extrapolation to the recovered gradient and demonstrate numerically that PPR combined with the Richardson extrapolation can reduce the interpolation and pollution errors simultaneously, and therefore, leads to an asymptotically exact a posteriori error estimator.

All theoretical findings are verified by numerical tests. READ MORE

Department of Mathematics Research Colloquium: Efficient time-domain DG methods for wave propagation

Event Date: October 26, 2016
Location: Clements Hall 126
Time: 3:30–4:30 (Refreshments are served 15 minutes before the talk)

Mathematics Colloquium Talk by Jesse Chan (Rice University)

Link for more information:

Contact: A. J. Meir

Event: Dynamics of Clean Foams, October 19

Event Date: October 19, 2016
Location: Clements Hall 126
Time: 3:30–4:30 (Refreshments are served 15 minutes before the talk)

Dynamics of Clean Foams. A Mathematics Colloquium Talk by Stephen Davis (Northwestern University.) For more information:

Or contact: A. J. Meir

SMU-trained physicist who bolstered Big Bang theory dies at 84

Dallas Morning News

Originally Posted: August 31, 2016

James Cronin, a Southern Methodist University graduate who shared a Nobel Prize for explaining why the universe survived the Big Bang, died last Thursday in St. Paul, Minn. He was 84.

His death was confirmed by the University of Chicago, where he was a professor emeritus. No cause was given.

In 1964, Cronin and Val Fitch of Princeton University were conducting experiments at Brookhaven National Laboratory on Long Island involving matter and antimatter: particles that have the same mass but hold opposite (though equal) charges, either positive or negative, compelling them to destroy each other on contact.

The researchers found that for all their similarities, the particles obeyed slightly different laws of physics: that there was, as Cronin put it, “a fundamental asymmetry between matter and antimatter.”

This contradicted a bedrock scientific principle known as charge-parity invariance, which had assumed that the same laws of physics would apply if the charges of particles were reversed from positive to negative or vice versa.

The finding, known as the Fitch-Cronin effect, bolstered the Big Bang theory, mainly by explaining why the matter and antimatter produced by the explosion did not annihilate each other, leaving nothing but light instead of a residue that evolved into stars, planets and people.

“We now believe this tiny difference led to us,” Michael S. Turner, an astrophysicist at the University of Chicago, said last year after Fitch died at 91.

James Watson Cronin was born in Chicago on Sept. 29, 1931. His father, also named James, met Cronin’s mother, the former Dorothy Watson, in a Greek class at Northwestern University. The elder James Cronin became a professor of Latin and Greek at SMU.

Cronin’s infatuation with physics began in high school. He graduated in 1951 from SMU, where he majored in physics and mathematics. He received a doctoral degree from the University of Chicago, where he studied under Enrico Fermi, Edward Teller and Murray Gell-Mann. His thesis was on experimental nuclear physics.

Cronin’s first wife, the former Annette Martin, died in 2005. He is survived by their children, Emily Grothe and Daniel Cronin; his second wife, the former Carol Champlin McDonald; and six grandchildren.

After collaborating with Cronin at Brookhaven, Fitch, the son of a Nebraska rancher, recruited him to Princeton. Cronin was lured back to the University of Chicago in 1971, attracted in part by one of the world’s most powerful particle accelerators, which was being built at what is now known as the Fermi National Accelerator Laboratory, operated by the university in partnership with a consortium of other educational institutions. He was offered a post teaching physics, astronomy and astrophysics.

Cronin and Fitch were awarded the Nobel Prize in Physics in 1980. But Cronin acknowledged that they had not completely solved a riddle of the universe.

“We know that improvements in detector technology and quality of accelerators will permit even more sensitive experiments in the coming decades,” he said at the time. “We are hopeful, then, that at some epoch, perhaps distant, this cryptic message from nature will be deciphered.”

Working with Fitch and using instruments they had devised, Cronin conducted his groundbreaking experiments when he was in his early 30s, less than a decade after he had received his doctorate. Why did it take the Nobel Committee 16 years to recognize their achievement?

“I don’t think that people recognized that this had something to do with one of the most fundamental aspects of nature, with the origin of the universe,” Cronin said in the 2006 book Candid Science VI: More Conversations With Famous Scientists, by Istvan Hargittai and Magdolna Hargittai. “I think that it took a while to realize this.”

He added: “For me, this was actually a good thing. I was much too young at that time to deal with such a thing as the Nobel Prize.” READ MORE

SMU Students Propose Innovation Community For Ex-Fraternity House


Originally Posted: May 4, 2016


Ingenuity is not limited to the hours of 9 to 5.

Providing a space where students can live and cultivate new ideas at any time of day is the driving force behind a pilot project being proposed by a group of students at Southern Methodist University in Dallas.

The living and learning community, dubbed Innovation House or iHouse, would welcome students across all academic disciplines and offer a platform to foster new products and businesses.

“The idea is we want to get people that have this raw passion or have a raw desire, and they’re driven enough to create projects and create their own designs,” said Momin Irfan, a freshman finance, computer science, and mathematics major at SMU. READ MORE

Scott A. Norris, Mathematics, on odds of winning $1.6B Powerball jackpot

Associated Press

Originally Posted: January 14, 2016

$1.6B Powerball jackpot to be split three ways

Winners bought their tickets in Florida, Tennessee and a Los Angeles suburb

An eye-popping and unprecedented Powerball jackpot whose rise to $1.6 billion became a national fascination will be split three ways.

The winners’ identities remain a mystery, but they bought their tickets in Florida, Tennessee and a Los Angeles suburb where even lottery losers were celebrating Thursday that such heady riches were won in their modest city.

The winners of the world-record jackpot overcame odds of 1 in 292.2 million to land on the numbers drawn Wednesday night, 4-8-19-27-34 and Powerball 10. They can take the winnings in annual payments spread over decades or a smaller amount in a lump sum.

The California ticket was sold at a 7-Eleven in Chino Hills, California, lottery spokesman Alex Traverso told The Associated Press. The winning ticket in Tennessee was sold in Munford, north of Memphis, according to a news release from lottery officials in that state.

The California store and its surrounding strip mall immediately became a popular gathering spot in the usually quiet suburb of 75,000 people. Hundreds of people, from news crews to gawkers, crowded the store and spilled into its parking lot.

They cheered and mugged for TV cameras as if it were New Year’s Eve or a sporting event. Many chanted, “Chino Hills! Chino Hills!” in celebration of the city.

“It’s history. We’re all so excited for our city,” Rita Talwar, 52, who has lived in Chino Hills for 30 years, told the local newspaper, the San Bernardino Sun.

Some took selfies with the store clerk on duty, who became an instant celebrity and may well have been the man who sold the ticket after being on duty for much of the run-up to Wednesday night’s drawing. READ MORE

Scott Norris, Mathematics, has one good tip for winning the Powerball jackpot

WINA News Radio

Originally Posted: January 8, 2016

It’s easy to sum up your chances of winning tomorrow’s huge Powerball jackpot: slim to none.

The math whizzes put the odds of winning at more than one in 292 million.

One statistical expert at the University at Buffalo – Jeffrey Miecznikowski – says that’s like flipping a quarter and getting heads 28 times in a row. In other words, forget it.

Scott A. Norris, an assistant professor of mathematics at Southern Methodist University, has one tip: He says let the computer pick rather than choosing the numbers yourself.

That’s because when people use birthdates or other favorite figures, they generally choose numbers 31 or below. That ignores the fact that there are 69 numbered balls. READ MORE

Four student projects win recognition (and $5,000) in SMU’s 2015 Big iDeas Business Plan Competition

Congratulations to Hunter Rice, Edward Allegra and Rax Friman on their winning projects. These Dedman College students were part of four student teams that competed in SMU’s Big iDeas Business Plan Competition.

More on the competition and the projects below:

Four student teams combined winning pitches with solid business plans to earn $5,000 startup grants for their projects through SMU’s Big iDeas program on Jan. 30, 2015.

The four winning teams were chosen from a business plan competition featuring the winners of the Big iDeas Pitch Competition, which took place in October.

The projects were judged by a panel of volunteers from Executives in Action, a Dallas-area organization that helps strengthen North Texas nonprofits by matching them with senior-level executives for pro bono consulting services. The winners:

The projects were judged by a panel of volunteers from Executives in Action, a Dallas-area organization that helps strengthen North Texas nonprofits by matching them with senior-level executives for pro bono consulting services. The winners:

Beyond US Clothing (Hunter Rice and J.P. Buxbaum) – a for-profit clothing company that partners with charities to help underprivileged children in the United States by offering unique T-shirt designs for each partnership and donating a portion of the sales to charities with a focus on children and education.

Biolum Sciences (Edward Allegra, Miguel Quimbar and Jack Reynolds) – A smartphone-based imaging system that can detect the presence of asthma and reduce the current 40% misdiagnosis of asthma in the United States.

Helpple (Austin Wells and Irisa Ona) – an app that connects people who need help with people who are offering to help, ranging from tutoring to moving furniture to getting volunteers.

Out & About (Renita Thapa, Sam Hubbard and Raz Friman) – an app that promotes local businesses and organizations by showing its users what is going on in the community for easy planning, exploring and getting to know the area.

“The world needs big thinkers to address global challenges. It needs innovators to create solutions. It needs risk-takers to turn solutions into sustainable businesses. And at SMU, Big iDeas makes this happen,” said Engaged Learning Director Susan Kress, whose office also oversees Big iDeas.

The students will spend the next nine months developing their projects. They will present results in October 2015 at Big iDeas Demo Day for a chance to win another $5,000 to continue their work.


• Visit SMU’s Big iDeas website at