Yuri Bazilevs is the E. Paul Sorensen Chair in the School of Engineering at Brown University. He was previously a Full Professor and Vice Chair in the Structural Engineering (SE) Department, and an Adjunct Full Professor in the Mechanical and Aerospace Engineering (MAE) Department, in the Jacobs School of Engineering at UCSD. He joined UCSD as an Assistant Professor in July of 2008, was promoted to Associate Professor with tenure in July 2012, and, subsequently, to Full Professor in July 2014. Yuri completed his PhD and Postdoc training, in 2006 and 2008, respectively, at UT Austin's Institute for Computational Engineering and Sciences (ICES).
Statement
Over a decade ago, Computational Science has been identified as “the third pillar of scientific method”, alongside with theory and experimentation, which are considered to be the two original pillars of scientific discovery [1]. It is now safe to say that Computational Science and Engineering (CSE) has “come of age”, and today presents a thriving enterprise that involves the development and use of computational algorithms, and their implementation in the environment of High Performance Computing (HPC), to translate mathematical models of physical phenomena into computer models that ultimately attempt to predict the future. CSE has been successful in a broad and increasing list of scientific and technological developments in basic science, engineering, and medicine, and also presents an integral and ever growing part of many agencies research and development programs.
However, as CSE matured, the development of modeling and simulation methods for basic sciences has taken a different path from that of engineering applications. The development of modeling and simulation methods for scientific discovery is focused on elucidating new scientific phenomena in natural or man-made physical systems. In the case of continuum systems, such as solids or fluids, the term “modeling” is often understood as the development, from experimental or observation data, of the novel constitutive relations, such as, for example, interaction potentials, rate-dependent forms of plastic and damage laws, shock and eddy viscosities, etc. The issues of geometric complexity, realistic boundary conditions, topological changes in the problem domain due to fragmentation or contact, etc., are often secondary and thus seldom addressed. Conversely, modeling and simulation in support of engineering design is focused on complex-geometry methods and efficiency of the discretization approaches. The issues of realistic boundary conditions and problem-domain motion become the primary drivers of methods development, and the fundamental physics/mechanics is often traded for empirical models that best fit the computational framework developed for a given application. Models that are easily implemented and that are “inexpensive” to execute are often preferred, especially when a large number of analyses is needed to support design.
Nevertheless, the initially divergent paths that modeling and simulation developments have taken in the science and engineering fields are starting to merge. On the one hand, cutting-edge science is becoming increasingly interested in applications involving complex geometry and coupled mechanical phenomena. For example, analysis of metamaterials, which derive their favorable mechanical properties from a specific topological and geometric arrangement of their substructures, relies more and more heavily on complex-geometry discretization methods. Coupled phenomena, such as fluid-solid or fluid-structure interaction (FSI) [2], are essential for accurate modeling of biological cell structures or that of materials subjected to high-strain-rate air-blast loading. On the other hand, the low accuracy of empirical models, which are often employed outside their limited range of applicability, is nowadays seldom compatible with the precision demands of modern engineering. This is especially true in the defense sector. In recent years, in several engineering applications, empiricism is often traded for fundamental, first- principle-based scientific theories. For example, in the area of solids and structures the development of multiscale computational methods is now enabling accurate, efficient, and, most importantly, predictive modeling of structures comprised of complex materials, such as concrete or laminated fiber-reinforced composites. In the area of fluids, large-eddy simulation approaches based on the so-called variational multiscale methods, which make no assumptions about the problem geometry or flow regime, are starting to be routinely employed for engineering-scale aerodynamic and hydrodynamic analyses.
While HPC has played a tremendous role in raising the quality and fidelity of computational simulations in science and engineering, 10-15 years ago a new concept of the so-called Dynamic-Data-Driven Application Systems (DDDAS) [3] has emerged that further changed the way CSE is approached these days. DDDAS is a framework in which dynamic and/or static sensor and measurement data collected for a given physical system is used to dynamically update a simulation model of that system. Using measurement data, the model geometry, boundary conditions, forcing, material parameters, etc., may be updated to better represent physical reality. At the same time, the properly updated computational model is able to produce higher-fidelity outputs for the quantities of interest for which measurements are not available, and further steer data measurement through appropriate placement of sensors. As such, DDDAS is a framework in which measurement and simulation co-exist in a symbiotic environment, which further enhances the predictive power of simulation methods.
These convergent demands that science and engineering applications place on the modeling and simulation methods today create an opportunity to rethink how these methods are developed and employed in academia, industry, and research labs. In his reserch work, Yuri addresses these demands by developing a first-of-its-kind, unified, predictive modeling framework that incorporates first-principle-based approaches, enables new scientific discovery, and possesses the accuracy, robustness, and efficiency attributes necessary to support modern engineering analysis and design. The PI envisions taking Isogeometric Analysis (IGA) [4], of which he is one of the original developers, as the foundational methodology for the following reasons:
IGA was proposed in an effort to “bridge the gap” between Computer-Aided Design (CAD) and the Finite Element Method (FEM) routinely employed in Computer-Aided Engineering (CAE). As such, at its foundation, IGA, unlike other computational technology, has a strong link to CAD and, as a result, engineering design.
IGA is function-based computational methodology, which, like FEM, relies on the weak or variational statement of the boundary value problem. As such, IGA is compatible with FEM on several levels: a. Under certain assumptions on the discretization, IGA reduces to standard FEM; b. IGA may be “coupled” with FEM in a straightforward fashion, which is especially useful for multiphysics applications like FSI. This compatibility is important for integration of IGA into existing analysis frameworks, and essential for adoption by users interested in IGA for their applications.
For the discretization of the solution fields, IGA makes use of splines, which are piece- wise polynomial functions joined with higher-order continuity. For many problems, arising in both science and engineering, the higher-order nature of splines gives high per- degree-of-freedom accuracy necessary to resolve the spatially multiscale phenomena present in many physical systems. In addition, the increased continuity of the basis functions gives rise to superior robustness necessary for engineering applications. As such, IGA has this rare combination of accuracy and robustness, which is well suited for the proposed modeling and simulation framework that treats science and engineering applications in a unified manner.
The PI and his team are pursuing research and development of novel core and special computational methods, where IGA plays a central role as the key unifying concept for CSE. The methods development is driven by advanced applications coming from academia, industry, and national lab collaborations, thus making the corresponding partnerships an essential component of this effort.
References
[1] D.A. Reed et al., “Computational Science: Ensuring America's Competitiveness”, PITAC Report, Arlington, VA, 2005.
[2] Y. Bazilevs, K. Takizawa, and T.E. Tezduyar, “Computational Fluid-Structure Interaction: Methods and Applications”, Wiley 2013.
[3] F. Darema. Dynamic data driven applications systems: A new paradigm for application simulations and measurements. In proceedings of ICCS 2004 4th International Conference on Computational Science, pages 662–669, 2004.
[4] J.A. Cottrell, T.J.R. Hughes, and Y. Bazilevs, “Isogeometric Analysis. Toward Integration of CAD and FEA”, Wiley 2009.
Computational Modeling of Free-Surface Fluid-Object Interaction for Coastal hydraulic Applications; Sponsor: Army Research Office (ARO); Amount: $50,000; Dates: 07/01/2010-03/31/2011.
A Pipeline for Patient-Specific Cardiovascular Modeling: Imaging, Simulation and Visualization; Sponsor: UCSD Chancellor’s Grant; Amount: $60,000; Dates: 06/01/2009-05/31/2010.
A Pipeline for Patient-Specific Cardiovascular Modeling: Imaging, Simulation and Visualization; Sponsor: UCSD Chancellor’s Grant; Amount: $60,000; Dates: 06/01/2010-05/31/2011.
Los Alamos - UC San Diego Educational Collaboration - Phase VII – Computational Fluid-Structure Interaction Simulation of Wind Turbines; Sponsor: Los Alamos National Security, LLC; Amount: $40,295; Dates: 10/01/09 - 09/30/10.
Los Alamos - UC San Diego Educational Collaboration - Phase VIII – Computational Fluid-Structure Interaction Simulation of Wind Turbines; Sponsor: Los Alamos National Security, LLC; Amount: $53,725; Dates: 10/01/10 - 09/30/11.
Free-Surface Fluid-Object Interaction for the Large-Scale Computation of Ship Hydrodynamics Phenomena; Sponsor: Army Research Office (ARO); Amount: $244,447; Dates: 05/01/11 – 04/30/14.
CAREER: Fluid-Structure Interaction and High Performance Computing for Wind Energy Applications; Sponsor: National Science Foundation (NSF); Amount: $458,838; Dates: 05/01/11 – 04/30/16.
DDDAS: Computational Steering of Large-Scale Structural Systems Through Advanced Simulation, Optimization, and Structural Health Monitoring; Sponsor: Air Force Office of Scientific Research (AFOSR); Amount: $695,905; Dates: 01/01/12 – 12/31/15.
Los Alamos - UC San Diego Educational Collaboration - Phase IX – Isogeometric Methods for Lagrangian Hydrodynamics; Sponsor: Los Alamos National Security, LLC; Amount: $101,115; Dates: 09/01/11 – 10/31/12.
Applications of Quantum Computing in Aerospace Science and Engineering; Sponsor: Air Force Office of Scientific Research (AFOSR); Amount: $3,750,000 (Co-PI, my share $400,000); Dates: 09/01/11 – 08/31/16.
CDS&E: A Large-Scale Data Discovery Framework For Understanding Intermittent, Performance-Critical Phenomena In Simulations Of Off-Shore Wind Turbines; National Science Foundation (NSF); Amount: $500,000 (Co-PI, my share $170,000); Dates: 09/01/13 - 08/31/16.
Fluid—Structure Interaction Simulation of Gas Turbine Engines Using Isogeometric Analysis; Sponsor: Army Research Office (ARO); Amount: $440,000; Dates: 01/01/14 - 6/14/18.
Progressive Damage Modeling for Combined Impact and Compressive Residual Strength Prediction; Sponsor: NASA; Amount: $1,085,500 (Co-PI, my share $450,000): Dates: 10/01/15 – 9/30/19.
Multiscale DDDAS with Emphasis on Aerospace Structures and Application to Unmanned Aerial Vehicles; Sponsor: Air Force Office of Scientific Research (AFOSR); Amount: $736,000; Dates: 10/01/15 – 3/15/19.
Improving Particle-Grid Methods; Sponsor: Los Alamos National Security, LLC; Amount: $67,658; Dates: 4/1/17 – 12/1/17.
Improving Particle-Grid Methods; Sponsor: Los Alamos National Security, LLC; Amount: $75,000; Dates: 1/1/18 – 9/30/18.
LES and RANS Simulations of Estuarine Flows: Understanding and Parameterizing the Role of Langmuir Turbulence; National Science Foundation (NSF); Amount: $178,177; Dates: 08/15/18 - 07/31/2021.
Implementation of NURBS into Cartablanca; Sponsor: Los Alamos National Security, LLC; Amount: $45,000; Dates: 6/8/19 – 12/31/19.
Assessment of meshless methods for the open room closure problem; Sponsor: Sandia National Laboratories; Amount $150,000; Dates 7/23/2019 – 12/31/2019.
Immersed Method Research and Development; Sponsor: Sandia National Laboratories; Amount $150,000; Dates 11/19/2019 – 9/18/2019.
Development of Peridynamics Models for Ductile Fracture and Blast Loading; Sponsor: Sandia National Laboratories; Amount $295,900; Dates 1/1/2020 – 9/30/2021.
Predictive Modeling and Simulation for Next Generation Naval Undersea Vehicles and Platforms; Sponsor: Office of Naval Research; Amount $1,845,000; Dates 7/1/2021 – 6/30/2024.
Undersea Vehicle Science and Technologies: Multifunctional Structural Batteries, Computationally Designed Materials and Additive Manufacturing Research Project; Sponsor: Office of Naval Research; Amount $1,815,000 (Co-PI, my share $330,000); Dates 7/1/2021 – 6/30/2024.
Predictive Modeling and Simulation for Next Generation Naval Undersea Vehicles and Platforms; Sponsor: Office of Naval Research; Amount $2,788,000; Dates 6/1/2023 – 5/31/2026.
PLENARY, SEMI-PLENARY AND NAMED LECTURES
Y. Bazilevs, “3D Simulation of Wind Turbine Rotors at Full Scale: Geometry Modeling, Aerodynamics and Fluid-Structure Interaction”, Plenary Lecture, Maths & Air 2010, Zaragoza, Spain, June 16-18, 2010.
Y. Bazilevs, “Enabling Computational Technology for Offshore Wind Turbines”, Plenary Lecture at the IVth International Conference on Computational Methods in Marine Engineering (MARINE2011), Lisbon, Portugal, Sept. 28-30, 2011.
Y. Bazilevs, “Fluid—Structure Interaction Modeling for Offshore Wind Turbines”, Plenary Lecture at IXth Deep Sea Offshore Wind R&D Seminar (DeepWind2012), Trondheim, Norway, January 19-20, 2012.
Y. Bazilevs, “Fluid-Structure Interaction Simulation of Wind Turbines at Full Scale”, Plenary Lecture at Young Investigators Conference (YIC2012), Aveiro, Portugal, April 24-27, 2012.
Y. Bazilevs, “Computational fluid-structure interaction: Blood pumps, surface ships, and wind turbines”, Semi-Plenary Lecture, ACM 2013 – A Conference Celebrating the 70th Birthday of Thomas J.R. Hughes, San Diego, CA, February 24-27, 2013.
Y. Bazilevs, “Computational Fluid-Structure Interaction: From Blood Pumps to Wind Turbines”, Semi-Plenary Lectureat 12th US National Congress on Computational Mechanics (USNCCM 2013), Raleigh, NC, July 22-25, 2013.
Y. Bazilevs, Warren Lecture, “Isogeometric Analysis and Fluid—Structure Interaction for Wind Turbines”, Department of Civil and Environmental Engineering, University of Minnesota, February 28, 2014.
Y. Bazilevs, “FSI Modeling and Simulation of Onshore and Offshore Wind Turbines at Full Scale”, Plenary Lecture at ParCFD 2014, Trondheim, Norway, May 20-22, 2014.
Y. Bazilevs, “Computational FSI: Methods Developed and Computations Performed”, Semi-Plenary Lecture at FEF 2015, Taipei, Taiwan, March 16-18, 2015.
Y. Bazilevs, “Computational Fluid-Structure Interaction with Applications”, Plenary Lecture at Coupled Problems 2015, Venice, Italy, May 18-20, 2015.
Y. Bazilevs, “IGA: Some New Fundamental Developments and Advanced Applications”, Plenary Lecture at IGA 2015, Trondheim, Norway, June 1-3, 2015.
Y. Bazilevs, “Robust Solution Strategies for Fluid-Structure Interaction Problems with Applications”, Plenary Lecture at Domain Decomposition 2015, Jeju Island, South Korea, July 6-10, 2015.
Y. Bazilevs, “Recent Advances in Isogeometric Analysis and Fluid-Structure Interaction”, Plenary Lecture at 28thNordic Seminar on Computational Mechanics, Tallinn, Estonia, October 22-23, 2015.
Y. Bazilevs, “Flexible Fluid-Structure Interaction Framework with Applications”, Semi-Plenary Lecture at FEF 2017, Rome, Italy, April 5-7, 2017.
Y. Bazilevs, “Flexible FSI: From Wind Turbines to Air Blast”, Plenary Lecture at International Conference on Advances in Computational Mechanics 2017, Phu Quoc Island, Vietnam, August 2-4, 2017.
Y. Bazilevs, “IGA as Enabling Technology for Engineering-Scale Simulations in Fluids, Solids, and FSI”, Plenary Lecture at IGA 2017, Pavia, Italy, September 11-13, 2017.
Y. Bazilevs, “IGA of Solids, Structures, and FSI: From Early Results to Recent Developments”, Plenary Lecture at Texas Applied Mathematics and Engineering Symposium (TAMES) 2017, Austin, TX, September 21-23, 2017.
Y. Bazilevs, “Recent Advances in IGA for FSI: Air-Blast FSI – Framework and Applications”, Semi-Plenary Lecture at ECCM - ECFD 2018 - 6th European Conference on Computational Mechanics (Solids, Structures and Coupled Problems) & 7th European Conference on Computational Fluid Dynamics, Glasgow, Scotland, June 11-15, 2018.
Y. Bazilevs, “Isogeometric Methods for Extreme-Event Simulation: Air-Blast FSI – Framework and Applications”, Semi-Plenary Lecture at WCCM 2018 – 13th World Congress on Computational Mechanics & 2nd Pan American Congress on Applied Mechanics, New York, New York, July 22-27, 2018.
Y. Bazilevs, “Isogeometric Methods for Extreme-Event Simulation: Air-Blast FSI – Framework and Applications”, Plenary Lecture at NewMech 2018, Providence, RI, September 29, 2018.
Y. Bazilevs, “Impact of IGA in Structures and FSI: From Early Results to Recent Developments”, Plenary Lecture at TWSM 2018 – Celebrating the 60th Birthday of Prof. K.M. Mathisen, Trondheim, Norway, December 12, 2018.
Y. Bazilevs, “IGA and RKPM: A Beautiful Friendship”, Plenary Lecture at Meshfree Methods and Advances in CM – Workshop Celebrating JS Chen’s 60th Birthday, Livermore, CA, March 10-12, 2019.
Y. Bazilevs, “Flexible FSI: From Wind to Air Blast”, Special Keynote Lecture at EMI 2019, Caltech, June 18-21, 2019.
Y. Bazilevs, “Recent Advances in Coupled Isogeometric-Meshfree Methods for Extreme-Event Simulation”, Annual Lecture at DCAMM 50th Anniversary Symposium, DTU, Copenhagen, Denmark, November 7, 2019.
Y. Bazilevs, “Isogeometric Analysis of Structures: Breakthroughs in Shell Modeling”, Lindbergh Lecture, University of Wisconsin, October 8, 2020.
Y. Bazilevs, “Advanced and Practical FSI for Large-Scale Structural Systems”, Annual Objective Resilience Lecture, Engineering Mechanics Institute of the ASCE, December 8, 2020.
Y. Bazilevs, “Recent Developments in Immersed IGA-Meshfree Methods for Extreme-Event Simulation”, Semi-Plenary Lecture, COMPSAFE 2020, Kobe, Japan, December 8-11, 2020.
Y. Bazilevs, “Isogeometric Analysis of Solids and Structures: Breakthroughs in Shell Modeling”, Distinguished Public Lecture, Department of Civil Engineering, University of Hong Kong, March 24, 2021.
Y. Bazilevs, “Breakthroughs in the Modeling of Shell Structures: IGA and Beyond”, Plenary Lecture, VIGA 2021, Lyon, France, September 26-29, 2021.
Y. Bazilevs, “Breakthroughs in the Modeling of Shell Structures: From IGA to Peridynamics”, MAE Distinguished Lecture, Department of Mechanical and Aerospace Engineering, The George Washington University, November 18, 2021.
Y. Bazilevs, “Thin Shells: From IGA to Peridynamics”, Semi-Plenary Lecture, ECCOMAS 2022, Oslo, Norway, June 5-9, 2022.
Y. Bazilevs, “Stabilized and Multiscale Methods: Unifying CFD for Science and Engineering”, Semi-Plenary Lecture, CFC 2023, Cannes, France, April 25-28, 2023.
Y. Bazilevs, “Computational Fluid-Structure Interaction: Methods, Breakthroughs and Applications”, Plenary Lecture, ICAM 2023, Hong Kong, May 30 – June 3, 2023.
Y. Bazilevs, “Recent Advances and Breakthroughs in the Modeling and Simulation of Extreme Events”, Plenary Lecture, EMI 2023, Atlanta, GA, June 6 – June 9, 2023.
Y. Bazilevs, “Recent Advances in IGA for Undersea Mechanics”, Plenary Lecture, ACM 2023/CFSI 2023, Austin, TX, October 22-25, 2023.
Y. Bazilevs, “Isogeometric Analysis: Breakthroughs in Computational Mechanics of Shell Structures”, Plenary Lecture, IMECE 2023, New Orleans, LA, October 29 – November 2, 2023.
Y. Bazilevs, “Taylor-Series Expansion for Meshfree Methods in Computational Solid Mechanics”, Plenary Lecture, Particle Methods and Applications Conference, Santa Fe, NM, January 22 – 24, 2024.
Y. Bazilevs, “Isogeometric Shells with Emphasis on Modeling of Architected Structures”, Semi-Plenary Lecture, 16th World Congress on Computational Mechanics (WCCM), Vancouver, Canada, July 21 – 26, 2024.
Y. Bazilevs, “Advanced and Practical Computational Fluid-Structure Interaction”, Distinguished Seminar, Department of Mechanical Engineering, Purdue University, August 29, 2024.
| Year | Degree | Institution |
|---|---|---|
| 2006 | PhD | University of Texas |
| 2001 | MS | Rensselaer Polytechnic Institute |
| 2000 | BS | Rensselaer Polytechnic Institute |
| Postdoctoral Fellow and Lecturer | University of Texas at Austin, Institute for Computational Engineering and Sciences (ICES) | 2006-2008 | Austin, TX, USA |
| Graduate Research Assistant | University of Texas at Austin, Computational Engineering and Science | 2002-2006 |
2002 Michael A. Sadowsky Prize for Best MS Thesis in Mechanics, RPI.
2004 Continuing Education Fellowship, UT-Austin.
2006 J.T. Oden ICES Postdoctoral Fellowship, ICES, UT Austin.
2007 Outstanding PhD Dissertation Nominee, UT Austin.
2009 “Most Cited Author in 2005-2008” Award from Computer Methods in Applied Mechanics and Engineering
2010 Hellman Fellow
2010 International Association for Computational Mechanics (IACM) Young Investigator Award
2011 NSF CAREER Award
2011 Gallagher Young Investigator Award from the US Association of Computational Mechanics (USACM)
2012 ASME Applied Mechanics Division Thomas J.R. Hughes Young Investigator Award
2013 Adviser of the UCSD Chancellor’s Dissertation Medal in Engineering PhD Thesis of Dr. Ming-Chen Hsu
2014 Warren Lecture, Department of Civil and Environmental Engineering, University of Minnesota
2014 Thomson Reuters Highly Cited Researcher (Computer Science)
2015 Fellow of USACM
2015 Thomson Reuters Highly Cited Researcher (Computer Science)
2015 Thomson Reuters Highly Cited Researcher (Engineering)
2016 Thomson Reuters Highly Cited Researcher (Computer Science)
2016 Thomson Reuters Highly Cited Researcher (Engineering)
2017 Clarivate Analytics Highly Cited Researcher (Computer Science)
2017 Clarivate Analytics Highly Cited Researcher (Engineering)
2018 ASCE Walter E. Huber Research Prize
2018 Clarivate Analytics Highly Cited Researcher (Computer Science)
2018 Clarivate Analytics Highly Cited Researcher (Engineering)
2018 Springer book titled “Frontiers in Computational Fluid-Structure Interaction and Flow Simulation: Research from Lead Investigators under Forty – 2018” dedicated to Y. Bazilevs and K. Takizawa in celebration of their 40th birthday
2019 Fellow of the Engineering Mechanics Institute (EMI) of the ASCE
2019 Clarivate Analytics Highly Cited Researcher (Computer Science)
2019 Annual Speaker of the Danish Center for Applied Mathematics and Mechanics
2019 Highest Cited Paper Award from the Journal of Advanced Engineering and Computation
2020 Lindbergh Lecture, Department of Mechanical Engineering, U of Wisconsin, Madison
2020 Gustus L. Larson Memorial Award from the ASME
2020 Annual Objective Resilience Lecture, Engineering Mechanics Institute of the ASCE
2021 ASME Materials Division Centennial Mid-Career Award
2021 Distinguished Public Lecture, Civil Engineering, University of Hong Kong
2021 Distinguished Lecture, Mechanical and Aerospace Engineering, George Washington U
2022 International Association for Computational Mechanics (IACM) Computational Mechanics Award
2022 Journal of Mechanics Best Paper Award
2024 Elected Fellow of the American Institute for Medical and Biological Engineering (AIMBE)
2024 Distinguished Seminar Lecture, School of Mechanical Engineering, Purdue University
| Name | Title |
|---|---|
| Bessa, Miguel | Associate Professor of Engineering |
| Gao, Huajian | Walter H. Annenberg Professor Emeritus of Engineering |
| Guduru, Pradeep | Professor of Engineering |
| Harris, Daniel | Associate Professor of Engineering |
| Srivastava, Vikas | Associate Professor of Engineering |
ASME Applied Mechanics Division (ASME-AMD)
US Association for Computational Mechanics (USACM)
International Association for Computational Mechanics (IACM)
ASCE Engineering Mechanics Institute (ASCE-EMI)
US National Committee for Theoretical and Applied Mechanics (USNC/TAM)
Yuri teaches undergraduate and graduate courses in the areas of solid and structural mechanics, focusing on computational methods in these areas.
| ENGN 0040 - Dynamics and Vibrations |
| ENGN 1300 - Structural Analysis |
| ENGN 2340 - Computational Methods in Structural Mechanics |
| ENGN 2911V - Advanced Topics in Computational Mechanics: Isogeometric Analysis, Meshfree Methods, and FSI |
| ENGN 2912N - Isogeometric Methods in Computational Mechanics |
