The meshfree MEGA code (Meshfree Explicit Galerkin Analysis code) I've built from the ground up since coming to Penn State is up and running with (nearly) state-of the art in RKPM.
Here's a demo problem. Quasi-linear Reproducing Kernel Particle Method (RKPM) [1-3] with Naturally Stabilized Nodal Integration (NSNI)  for slope stability analysis. Soil is modeled with Drucker-Prager with tension cut-off.
Variationally Consistent Integration (VCI)  to be added soon.
 Liu, Wing Kam, Sukky Jun, and Yi Fei Zhang. "Reproducing kernel particle methods." International journal for numerical methods in fluids 20.8‐9 (1995): 1081-1106.
 Chen, Jiun-Shyan, et al. "Reproducing kernel particle methods for large deformation analysis of non-linear structures." Computer methods in applied mechanics and engineering 139.1-4 (1996): 195-227.
 Yreux, Edouard, and Jiun‐Shyan Chen. "A quasi‐linear reproducing kernel particle method." International Journal for Numerical Methods in Engineering 109.7 (2017): 1045-1064.
 Hillman, Michael, and Jiun‐Shyan Chen. "An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics." International Journal for Numerical Methods in Engineering 107.7 (2016): 603-630.
 Chen, Jiun‐Shyan, Michael Hillman, and Marcus Rüter. "An arbitrary order variationally consistent integration for Galerkin meshfree methods." International Journal for Numerical Methods in Engineering 95.5 (2013): 387-418.
Our CEE Snapshot:
U.S. News Rankings
Undergraduate – Civil: 14
Undergraduate – Environmental: 13
Graduate – Civil: 17
Graduate – Environmental: 17
NSF ranking for total research expenditures in science and engineering: 16
NSF Career Award Recipients: 9
2016-17 Research Expenditures: $16 million
Penn State article released today about the work I'm doing with Chuck Bakis.
My RKPM encyclopedia with Wing Kam Liu, JS Chen, and Sheng-Wei Chi is published.
Chen, J.-S., Liu, W. K., Hillman, M. C., Chi, S.-W., Lian, Y. and Bessa, M. A. (2018) “Reproducing Kernel Particle Method for Solving Partial Differential Equations”, in ‘Encyclopedia of Computational Mechanics Second Edition’, edited by Erwin Stein , René de Borst and Thomas J. R. Hughes. Chichester, UK: John Wiley & Sons, Ltd, pp. 1-44.
I will be working on a project with Professor Chuck Bakis in the Engineering Science and Mechanics Department at Penn State, developing and validating a new meshfree formulation for fracture mechanics with application to analysis of FRP composites.
A paper I worked on with JS Chen is now available online. It presents a performance comparison between node-based Galerkin and collocation meshfree methods in terms of accuracy, efficiency, and stability:
Hillman, M., Chen, J. S., Performance Comparison of Nodally Integrated Galerkin Meshfree Methods and Nodally Collocated Strong Form Meshfree Methods, Advances in Computational Plasticity, Volume 46, pp 145-164, 2017.
It can be found here:
Last week, I gave a talk at the Department of Mathematics, Penn State University. The topic was Variational Crimes in Meshfree Methods. In this talk, two non-trivial variational crimes committed in the commonplace employment of meshfree methods were discussed. The information can be found here.
This month, a plenary lecture by J. S. Chen co-authored by me was given and I also gave a talk at the COMPLAS conference at Barcelona, Spain.
The topic of the plenary lecture was Recent Advances in Accelerated and Stabilized Meshfree Method for Modeling Man-made and Natural Disasters. The information can be found here.
The talk by me was "A Smoothed Implicit Gradient Reproducing Kernel Particle Method for Extreme Event Modelling." The information can be found here.
A paper I worked on with J.S. Chen is now available online. It studies how damage propagates between scales in concrete:
Liang, S., Chen, J. S., Li, J. , Lin, S. P., Roth, M. J., Heard, W., Hillman, M., Numerical investigation of statistical variation of concrete damage between scales, International Journal of Fracture, 2017.
Last Monday I give a keynote lecture at the Engineering Mechanics Institute Conference (EMI 2017) in San Diego. The topic of the presentation was Stable and Robust Meshfree Integration for Extreme Event Simulations.
I co-organized a symposium MS 23: Extreme Events Modeling with J. S. Chen (UCSD) and Jason Roth (Army ERDC).
I am also the coauthor of several presentations which you can find in the program.
Congratulations to J. S. Chen and Yuri Bazilevs for their successful conference!
And happy 80th birthday to Zdeněk Bažant!
An undergraduate mentor of mine, Dr. Binod Tiwari has won the Outstanding Professor Award, the highest honor for professors at CSUF. He is truly deserving of this award and I am happy to hear about his recognition. Congratulations Dr. Tiwari!
The press release can be found here:
A paper I worked on with JS Chen and Yuri Bazilevs' groups at UCSD is now availible online. It is about immersed meshfree methods for fluid structure interaction:
Bazilevs, Y., Moutsanidis, G., Bueno, J., Kamran, K., Kamensky, D., Hillman, M., Gomezc, H., Chen, J.S., A New Formulation for Air-Blast Fluid Structure Interaction Using an Immersed Approach. Part II: Coupling of IGA and Meshfree Discretizations, Computational Mechanics, 2017, doi:10.1007/s00466-017-1395-2.
A paper on studying damage between scales in concrete has also been accepted in the International Journal of Fracture:
Liang, S., Chen, J. S., Li, J. , Lin, S. P., Roth, M. J., Heard, W., Hillman, M., Numerical investigation of statistical variation of concrete damage between scales, International Journal of Fracture, accepted.
My review paper on meshfree methods "Meshfree Methods: Progress Made after 20 Years" has been published in ASCE's Journal of Engineering Mechanics. It extensively covers the history of meshfree methods, provides a state-of-the-art review, and introduces for the first time the explicit relationship between MLS/RK, generalized finite differences, diffuse elements, implicit gradient methods, synchronized derivative methods, and Peridynamics.
My alma mater California State University Fullerton (CSUF) wrote an article about me in their magazine TITAN for the Spring 2017 issue, which can be found on p28.
In Spring 2017, I will teach a new course (CE 597) Meshfree Methods & Advanced Computational Solid Mechanics. It will cover the following topics: Meshfree methods (Galerkin, collocation), eXtended and generalized finite element and other PU methods, isogeometric analysis, large deformation analysis of nonlinear structures, constitutive models, inelasticity, methods for plates and shells, methods for fracture, incompressable materials. Eulerian description of conservation laws. Stability, accuracy and convergence.
My book chapter "An Implicit Gradient Meshfree Formulation for Convection-Dominated Problems" in Advances in Computational Fluid-Structure Interaction and Flow Simulation is now published and is available online:
Meshfree approximations are ideal for the gradient-type stabilized Petrov–Galerkin methods used for solving Eulerian conservation laws due to their ability to achieve arbitrary smoothness, however, the gradient terms are computationally demanding for meshfree methods. To address this issue, a stabilization technique that avoids high order differentiation of meshfree shape functions is introduced by employing implicit gradients under the reproducing kernel approximation framework. The modification to the standard approximation introduces virtually no additional computational cost, and its implementation is simple. The effectiveness of the proposed method is demonstrated in several benchmark problems.
My paper "A stabilized nodally integrated meshfree formulation for fully coupled hydro-mechanical analysis of fluid-saturated porous media" is now published and is available online:
Numerical modeling of reservoirs with low permeability or under undrained conditions often suffers from spurious fluid pressure oscillations due to the improper construction of approximation spaces. To address this issue, a fully coupled, stabilized meshfree formulation is developed based on a fluid pressure projection method, in which an additional stabilization term is added to the variational equation to correct the defi- ciency of the equal-order u –p reproducing kernel approximation. The projection scheme is formulated under the framework of the stabilized conforming nodal integration which enables a significant enhancement of the computational efficiency and accuracy, and the spurious low-energy modes of nodal integration are also eliminated. The effectiveness of the proposed stabilized meshfree formulation is demonstrated by solving several benchmark problems.
Penn State just released an article about my research, you can find it here.
Monday I gave a talk "Accelerated Meshfree Methods Under a Smoothed Implicit Gradient Framework," at the USACM Conference on Isogeometric Analysis and Meshfree Methods.
I also chaired 4 sessions and was the co-author for six other talks:
"A Riemann-SNNI Galerkin Meshfree Method for Solid and Fluid Dynamics," G. Zhou*, J.S. Chen, Michael Hillman
"A New Immersed Isogeometric- Meshfree Technique for Fluid-Structure Interaction Problems Involving High Mach Numbers, Part I," Jesus Bueno*, G. Moutsanidis, K. Kamran, Michael Hillman, H. Gomez, J.S. Chen, Y. Bazilevs
"A New Immersed Isogeometric- Meshfree Technique for Fluid-Structure Interaction Problems Involving High Mach Numbers, Part II," Jesus Bueno*, G. Moutsanidis, K. Kamran, Michael Hillman, H. Gomez, J.S. Chen, Y. Bazilevs
"Application of Meshfree Methods to Penetration and Blast Effects Modeling," J. Roth*, J. Sherburn, A. Frank, M. Hillman, J.S. Chen"
"Fragment-Impact Modeling of Concrete Structures," F. Beckwith*, M. Hillman, J.S. Chen
"RKPM Formulation for Fully Coupled Hydro- Mechanical Analysis of Fluid-Saturated Porous Media, Haoyan Wei*," J. S. Chen, Michael Hillman
Publications based on this research will be forthcoming.
I have been invited to help co-organize a minisymposia at the Engineering Mechanics Institute conference (EMI 2017) in San Diego next year June 4th - June 7th. My co-organizers are Jason Roth of ERDC and J.S. Chen of UC San Diego.
Abstracts can be submitted here starting October 1, 2016 until January 1, 2017.
The minisymposia will solicit all subjects related to computational methods and related experimental V&V for the study of extreme events, which include, but are not limited to, the following:
* Method and algorithm development for the simulation of problems involving harsh dynamic loading, high strain-rate, large material deformation, fracture and failure, or material breakup
* Fluid-structure interaction in disaster dynamics and material/structure failure
* Multiscale approaches to extreme material failure and disaster simulation
* Constitutive modeling and characterization of materials under high strain rate
* Constitutive modeling and characterization of disaster debris fields
* Simulation of multi-phase flow fields resulting from disaster events
* Applications of computational methods to simulation of natural disasters such as tsunamis, earthquakes, and landslides
* Applications of computational methods to simulation of manmade disasters like blast and penetration
* Computational investigations on infrastructure resiliency to include predictions of residual strength and prevention of progressive collapse
* Computational and experimental investigations on high-rate damage and failure mechanisms in semi-brittle geomaterials like concrete
* Computational and experimental investigations on soil liquefaction, foundation failure and debris flow
* Verification and validation of disaster simulation models
* Numerical algorithm implementation and simulation software development
* Large scale parallel computation and scalable algorithms
I will help organize of the Meshfree and Particle Methods minisymposia at the 2017 USNCCM conference, where I will also be the corresponding organizer. My co-organizers are JS Chen of UC San Diego, Zhen Chen of the University of Missouri, and Sheng-Wei Chi of the University of Illinois, Chicago.
Abstracts are open for submission November 1, 2016 – February 28, 2017 at http://14.usnccm.org/abstract-submission. Topics of interest include, but are not limited to the following:
Penn State has issued a press release about me joining the department:
Two new faculty members join civil and environmental engineering
I have officially started my position at Penn State as an Assistant Professor in the Civil and Environmental Engineering Department. I will also be holding the endowed position of the L Robert and Mary L Kimball Early Career Development Professorship. This year I will advise one PhD student and one post-doc.
I have co-authored a review article on meshfree methods along with JS Chen of UC San Diego, and Sheng-Wei Chi of the University of Illinois, Chicago. It has been accepted for publication and will appear in ASCE's Journal of Engineering Mechanics.
I will present "Accelerated Meshfree Methods Using Variationally Consistent Naturally Stabilized Nodal Integration" in the minisyposia Recent Advances in Galerkin and Collocation Meshfree Methods at WCCM 2016. Tomorrow I will present "RKPM with Quasi-linear Approximation for Fragment-Impact Modeling" for Edouard Yreux of LSTC in the same minisymposia, where I will also chair the session.
Thursday JS Chen will give a plenary lecture "Fracture to Damage Multiscale Modeling and Application to Extreme Events Simulation" where I am a co-author, along with Edouard Yreux, and Guohua Zhou (my post-doc).