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Alumni Xu Jinchao’s Work Leads to One of the Ten DOE Breakthroughs in Computational Science




Recently, a report released by Office of Advanced Scientific Computing Research in U.S. Department of Energy (DOE) identifies ten recent breakthroughs in computational science. The method for Maxwell’s equations proposed by Doctor Xu Jinchao of Penn State University and Doctor Hiptmair of ETH in Swiss, as the only numerical method, leads to one of the ten big breakthroughs. Doctor Xu Jinchao is a Chinese expert in Computational Mathematics. As one of our Outstanding Alumni and one of the special-employed “Lotus scholarship professors”, Doctor Xu serves as Director of Institute for Computational and Applied Mathematics of Xiangtan University and Director of Center for Computational Mathematics and Applications, Penn State.

A major advantage of Hiptmair-Xu (HX) method over the traditional methods is that its validity is little affected by the increase of the problem scale and the processor load. According to the result of numerous numerical experiments done by computational scientists from Lawrence Livermore National Laboratory (a U.S. Department of Energy national laboratory) such as Vassilevski and Kolev, the method outperforms earlier solution techniques by as much as 4 to 25 times. The new method can solve problems with complicated geometric shapes and with major discontinuous material coefficients.

This HX- method is the first one backed up by a solid theoretical framework and a scalable one applicable to Maxwells equations. The presentation and application of this method is a perfect example of how fundamental mathematical research can promote the development of scientific computing. The work Nodal auxiliary space preconditioning in H(curl) and H(div) spaces was published in SIAM J. Numer. Anal. (45:2483-2509), an authorized International Journal of Computational Mathematics. The project team in Xiangtan University was responsible for the three-dimensional numerical experiments in the work.

As an expert in the field of numerical solutions of partial differential equations, Prof. Xu Jinchao is among the mathematicians whose papers enjoy the highest citation rate. The BPX-preconditioner proposed by Xu in his early days has become one of the basic methods in the field of numerical solutions of partial differential equations, and the iterative framework based on space decomposition and subspace calibration exerts a profound influence and is regarded as the classic by his peers. The HX- method recently proposed by Xu and Hiptmair is the result of Xu’s research over years.