Openings
Research associates
No openings at this time.
Postdoctoral scholars
No openings at this time.
The Computational Mechanics and Optimization Lab has an opening for a
postdoctoral scholar is seeking a full-time postdoctoral researcher to
develop and implement high-order and reduced-order methods for high-speed flows.
Specifically, our aim is to mature novel CFD methodologies developed in our group
(implicit shock tracking and implicit feature tracking methods) and scale them to
relevant, large-scale high-speed flows. The project will require algorithmic innovation,
parallel implementation in our in-house code, and mentoring students. The duration of
the position is one year with possibility for extension based on performance.
Minimum Qualifications: (1) PhD in engineering, applied mathematics, etc., (2) Experience developing and implementing CFD methods, (3) Experience with grid generation for high-speed flows, (4) Experience with high-performance computing.
Desired Qualifications: (1) Experience with high-order methods, (2) Experience with nonlinear optimization, (3) Julia programming experience.
Interested applicants should send a CV and contact information for three professional references to Dr. Matthew J. Zahr (mzahr (at) nd.edu).
For more information, email Dr. Zahr.
Graduate students
The CaMOLab has openings for highly motivated graduate students interested
in developing numerical methods to solve relevant problems across a range
of disciplines in science, engineering, and medicine. Specific projects with
openings are described below along with desired qualifications; however, our
group is always interested in highly talented and motivated students.
If your background or interests do not align perfectly with any of the projects
below, but are broadly interested in the development of numerical methods for
science, engineering, or medical problems, you are encouraged to contact
Dr. Zahr to discuss potential opportunities.
To apply for any of these openings, review the
application information on the AME website and complete the
online application
through the graduate school and mention Dr. Zahr as a prospective
advisor in your application. The deadline
is Feb 1 for fall admission and Nov 1 for spring admission.
Due to the large number of applications, interested students are advised to
email Dr. Zahr to express interest in joining the group. Admission decisions
are only made upon receipt of a full application through formal channels.
Undergraduate students
The CaMOLab has openings for highly motivated undergraduate students interested in developing, testing, and using numerical methods to solve relevant problems across a range of disciplines in science, engineering, and medicine. Specific projects with openings are described below along with desired qualifications. However, our group is always interested in highly talented and motivated students. Students without the desired background will be considered provided they show interest/passion for the project and committment to developing the required skills. To apply for any of these openings, email Dr. Zahr to express interest in joining the group.
CaMOLab research
Research in the CaMOLab involves the development of novel numerical methods to solve relevant and challenging problems that arise in mathematics, engineering, science, or medicine. As such, it lies at the intersection of mathematics, engineering, and computer science and requires a broad set of skills, including: a solid foundation in mathematics, particularly advanced calculus and numerical analysis, programming (Python, Julia, Matlab, MPI parallelism), familiarity with Linux system and high-performance computing, and basic understanding of engineering physics.
High-order shock tracking for high-speed flow and combustion
This project involves the development, implementation, and maturation of high-order numerical methods for resolving non-smooth flow features (shocks, contacts, rarefactions) in hyperbolic conservation laws. It also involves applying these methods to solve challenging engineering problems including high-speed flows (transonic, supersonic, and hypersonic regimes) and combustion. For background information, see the project page and references therein. For additional information, email Dr. Zahr. Relevant background: coding experience in Julia and Python, familiarity with numerical methods for solving PDEs, e.g., finite element methods, and familiarity with numerical optimization (nonlinear, constrained). Openings: Undergraduate students, graduate students.
Adaptive model reduction
This project involves the development and implementation of new, adaptive reduced-order model methods for drastically reducing the computational cost of solving partial differential equations. For background information, see project page 1 or project page 2 and references therein. For additional information, email Dr. Zahr. Relevant background: coding experience in Julia and Python, familiarity with numerical methods for solving PDEs, e.g., finite element methods, and familiarity with projection-based reduced-order models. Openings: Undergraduate students, graduate students.
Optimization and computational fluid dynamics for superresolution MR images
This project involves the development and implementation of high-order numerical methods for solving biological flow and optimization-based data assimilation to improve the computational model using MRI data from clinical collaborators. This project will involve the development of a computational pipeline that begins with a 4D flow MR image (clinical data) and returns a computational fluid dynamics 4D flow solution that agrees with the data. This will involve segmentation and meshing using standard tools and implementation of new numerical methods for the computational fluid dynamics simulation and data assimilation. For background information, see project page and references therein. For additional information, email Dr. Zahr. Relevant background: coding experience in Julia and Python, familiarity with numerical methods for solving PDEs, e.g., finite element methods, familiarity with numerical optimization (nonlinear, constrained) and time-dependent PDE-constrained optimization (sensitivity, adjoint methods). Openings: Undergraduate students, graduate students.
High-order and reduced-order methods for topological optimization
This project has two distinct directions that involve the development of new numerical methods for topological optimization for optimal design of products that will be printed using additive manufacturing tools. The first direction will develop high-order methods for topological optimization to sharply represent the interface and accurately approximate the PDE solution. The second direction will develop adaptive reduced-order models to substantially reduce cost of topological optimization for fast prototyping and quick turnaround times in the manufacturing pipeline. For additional information, email Dr. Zahr. Relevant background: coding experience in Julia and Python, familiarity with numerical methods for solving PDEs, e.g., finite element methods, familiarity with numerical optimization (nonlinear, constrained), and experience with advanced topics such as topology optimization and level set methods. Openings: Undergraduate students, graduate students.
Other topics in computational physics
The CaMOLab is always interested in highly motivated graduate students broadly interested in developing numerical methods to solve relevant problems across a range of disciplines in science, engineering, and medicine.