Andrew Christlieb

Chair, Department of Computational Mathematics, Science and Engineering Michigan State University

  • East Lansing MI

Expert in Multi-scale modeling and high-order numerical methods

Contact

Michigan State University

View more experts managed by Michigan State University

Media

Biography

Andrew Christlieb received his Ph.D. from the University of Wisconsin-Madison in 2001. Upon completing his Ph.D., he took a postdoc in the Aerospace Department at the University of Michigan with Iain Boyd, working on the simulation of micro air foils. He then transitioned to a postdoc in the Mathematics Department at the University of Michigan, where he worked with Robert Krasny on the development of mesh-free methods for plasma simulations. Since 2004, he has worked very closely with the RDHE group at the Air Force research labs on the development of new methods for particle simulations of plasmas. In 2006, Christlieb joined the mathematics department at Michigan State University. In 2006, he was awarded a summer faculty fellow from the Air Force to work with AFRL Edwards on modeling of electric pupation. In 2007, he received the Air Force Young Investigator Award for his work on the development of novel methods for simulating plasmas. From 2008-2012, Christlieb was an IPA for the directed energy group at Kirtland Air Force Base. In 2010, he was promoted to associate professor and in 2014 he was promoted to professor. In 2015, he was named an MSU Foundation Professor.

Christlieb has an active research group, focusing on multi-scale modeling, high order numerical methods and sub-linear lossy compression algorithms. He is currently advising three postdocs and 10 students. His former Ph.D. students have gone on to work at national labs, industry and in academia. He has been involved in the development of a host of high order Eulerian, Lagrangian and semi-Lagrangian conservative methods for the kinetic simulation of plasmas, as well as the development of high order finite difference constrained transport methods for the simulation of magnetohydrodynamics targeted at AMR codes and new implicit Maxwell solvers targeting scale separation in plasmas. Christlieb's group is currently funded by AFOSR Computational Mathematics, AFOSR Physics and Electronics, AFRL RDHE, NSF Division of Mathematics and ORNL LDRD on scalable computing.

Industry Expertise

Education/Learning
Computer Software
Laboratory Services
Research

Areas of Expertise

Fast Convolution Methods
Multi-scale Modeling
High Order Numerical Methods
Weighted Essentially Non-oscillatory Methods
Defect Correction Methods
Sub-linear Lossy Compression Methods
Kinetic Theory
Plasmas Science
Energy Materials and Phase Filed Models

Accomplishments

Young Investigator Award

2007-01-01

U.S. Air Force

Education

University of Wisconsin

Ph.D.

Mathematics

2001

University of Wisconsin

M.S.

Applied Mathematics

1998

University of Michigan

B.S.

Electrical and Computer Engineering

1996

Show All +

News

First Graduate Fellowship in CMSE Department Established by MSU Alumnus

MSU Today  

2017-02-27

Andrew Christlieb, CMSE chair, said that the endowment is incredibly important to the department because it provides a mechanism for recruiting the best students.

“To build a world-leading department, we need talented graduate students who are enthusiastic about being here, and enthusiastic about what we’re doing,” Christlieb said. “This endowment gives us the ability to recruit that level of talent. It means a lot to us.”...

View More

Prestigious Research Fellowships Awarded to MSU College of Natural Science Faculty

MSU Today  

2016-02-24

Andrew Christlieb, mathematics professor and CMSE chair, was thrilled about Hirn’s selection as a Sloan fellow and the additional support it will lend to his innovative research.

“Matt’s work is unique in that he is developing next generation machine learning algorithms in order to address some of the most pressing and challenging problems arising in large scale computational modeling,” Christlieb said. “This aspect of Matt’s work makes him a critical link in CMSE, and really points to an untapped potential at the interface of computing and data science. We are truly honored that the Sloan Foundation has taken this opportunity to recognize one of our energetic, young scientists.”...

View More

MSU Recruiting 100 Scientists to Meet Global Challenges

WKAR  

2015-10-20

Michigan State University will hire 100 new faculty members to embark on a long-term effort to expand its scientific research profile. We talk with MSU’s Dr. Steven Hsu, Vice-President for Research and Graduate Studies, and Dr. Andrew Christlieb, chair of the new Department of Computational Mathematics, Science and Engineering...

View More

Journal Articles

Adaptive mesh refinement based on high order finite difference WENO scheme for multi-scale simulations

Journal of Computational Physics

2011

In this paper, we propose a finite difference AMR-WENO method for hyperbolic conservation laws. The proposed method combines the adaptive mesh refinement (AMR) framework and with the high order finite difference weighted essentially non-oscillatory (WENO) method in space and the total variation diminishing (TVD) Runge–Kutta (RK) method in time (WENO-RK) and by a high order coupling. Our goal is to realize mesh adaptivity in the AMR framework, while maintaining very high (higher than second) order accuracy of the WENO-RK method in the finite difference setting. The high order coupling of AMR and WENO-RK is accomplished by high order prolongation in both space (WENO interpolation) and time (Hermite interpolation) from coarse to fine grid solutions, and at ghost points. The resulting AMR-WENO method is accurate, robust and efficient, due to the mesh adaptivity and very high order spatial and temporal accuracy. We have experimented with both the third and the fifth order AMR-WENO schemes. We demonstrate the accuracy of the proposed scheme using smooth test problems, and their quality and efficiency using several 1D and 2D nonlinear hyperbolic problems with very challenging initial conditions. The AMR solutions are observed to perform as well as, and in some cases even better than, the corresponding uniform fine grid solutions. We conclude that there is significant improvement of the fifth order AMR-WENO over the third order one, not only in accuracy for smooth problems, but also in its ability in resolving complicated solution structures, due to the very low numerical diffusion of high order schemes. In our work, we found that it is difficult to design a robust AMR-WENO scheme that is both conservative and high order (higher than second order), due to the mass inconsistency of coarse and fine grid solutions at the initial stage in a finite difference scheme. Resolving these issues as well as conducting comprehensive evaluation of computational efficiency constitute our future work.

View more

Parallel high-order integrators

SIAM Journal on Scientific Computing

2010

In this work we discuss a class of defect correction methods which is easily adapted to create parallel time integrators for multicore architectures and is ideally suited for developing methods which can be order adaptive in time. The method is based on integral deferred correction (IDC), which was itself motivated by spectral deferred correction by Dutt, Greengard, and Rokhlin [BIT, 40 (2000), pp. 241–266]. The method presented here is a revised formulation of explicit IDC, dubbed revisionist IDC (RIDC), which can achieve pth-order accuracy in “wall-clock time” comparable to a single forward Euler simulation on problems where the time to evaluate the right-hand side of a system of differential equations is greater than latency costs of interprocessor communication, such as in the case of the N-body problem. The key idea is to rewrite the defect correction framework so that, after initial start-up costs, each correction loop can be lagged behind the previous correction loop in a manner that facilitates running the predictor and $M=p-1$ correctors in parallel on an interval which has K steps, where $K\gg p$. We prove that given an rth-order Runge–Kutta method in both the prediction and M correction loops of RIDC, then the method is order $r\times(M+1)$. The parallelization in RIDC uses a small number of cores (the number of processors used is limited by the order one wants to achieve). Using a four-core CPU, it is natural to think about fourth-order RIDC built with forward Euler, or eighth-order RIDC constructed with second-order Runge–Kutta. Numerical tests on an N-body simulation show that RIDC methods can be significantly faster than popular Runge–Kutta methods such as the classical fourth-order Runge–Kutta scheme. In a PDE setting, one can imagine coupling RIDC time integrators with parallel spatial evaluators, thereby increasing the parallelization. The ideas behind RIDC extend to implicit and semi-implicit IDC and have high potential in this area.

View more

A conservative high order semi-Lagrangian WENO method for the Vlasov equation

Journal of Computational Physics

2010

In this paper, we propose a novel Vlasov solver based on a semi-Lagrangian method which combines Strang splitting in time with high order WENO (weighted essentially non-oscillatory) reconstruction in space. A key insight in this work is that the spatial interpolation matrices, used in the reconstruction process of a semi-Lagrangian approach to linear hyperbolic equations, can be factored into right and left flux matrices. It is the factoring of the interpolation matrices which makes it possible to apply the WENO methodology in the reconstruction used in the semi-Lagrangian update. The spatial WENO reconstruction developed for this method is conservative and updates point values of the solution. While the third, fifth, seventh and ninth order reconstructions are presented in this paper, the scheme can be extended to arbitrarily high order. WENO reconstruction is able to achieve high order accuracy in smooth parts of the solution while being able to capture sharp interfaces without introducing oscillations. Moreover, the CFL time step restriction of a regular finite difference or finite volume WENO scheme is removed in a semi-Lagrangian framework, allowing for a cheaper and more flexible numerical realization. The quality of the proposed method is demonstrated by applying the approach to basic test problems, such as linear advection and rigid body rotation, and to classical plasma problems, such as Landau damping and the two-stream instability. Even though the method is only second order accurate in time, our numerical results suggest the use of high order reconstruction is advantageous when considering the Vlasov–Poisson system.

View more

Show All +