https://hdl.handle.net/1721.1/35730 2026-04-08T08:18:43Z 2026-04-08T08:18:43Z Dai, K.Y. Liu, Guirong https://hdl.handle.net/1721.1/35825 2019-04-12T08:06:33Z 2007-01-01T00:00:00Z

Smoothed Finite Element Method Dai, K.Y.; Liu, Guirong In this paper, the smoothed finite element method (SFEM) is proposed for 2D elastic problems by incorporation of the cell-wise strain smoothing operation into the conventional finite elements. When a constant smoothing function is chosen, area integration becomes line integration along cell boundaries and no derivative of shape functions is needed in computing the field gradients. Both static and dynamic numerical examples are analyzed in the paper. Compared with the conventional FEM, the SFEM achieves more accurate results and generally higher convergence rate in energy without increasing computational cost. In addition, as no mapping or coordinate transformation is performed in the SFEM, the element is allowed to be of arbitrary shape. Hence the well-known issue of the shape distortion of isoparametric elements can be resolved.

2007-01-01T00:00:00Z Huynh, Dinh Bao Phuong Peraire, Jaime Patera, Anthony T. Liu, Guirong https://hdl.handle.net/1721.1/35824 2019-04-12T08:35:47Z 2007-01-01T00:00:00Z

Reduced Basis Approximation and A Posteriori Error Estimation for Stress Intensity Factors: Application to Failure Analysis Huynh, Dinh Bao Phuong; Peraire, Jaime; Patera, Anthony T.; Liu, Guirong This paper reports the development of reduced basis approximations, rigorous a posteriori error bounds, and offline-online computational procedures for the accurate, fast and reliable predictions of stress intensity factors or strain energy release rate for “Mode I” linear elastic crack problem. We demonstrate the efficiency and rigor of our numerical method in several examples. We apply our method to a practical failure design application.

2007-01-01T00:00:00Z Li, Zirui Liu, Guirong Chen, Yuzong Wang, Jian-Sheng Hadjiconstantinou, Nicolas Cheng, Y. Han, J. https://hdl.handle.net/1721.1/35823 2019-04-12T08:35:45Z 2007-01-01T00:00:00Z

Linear Thermodynamics of Rodlike DNA Filtration Li, Zirui; Liu, Guirong; Chen, Yuzong; Wang, Jian-Sheng; Hadjiconstantinou, Nicolas; Cheng, Y.; Han, J. Linear thermodynamics transportation theory is employed to study filtration of rodlike DNA molecules. Using the repeated nanoarray consisting of alternate deep and shallow regions, it is demonstrated that the complex partitioning of rodlike DNA molecules of different lengths can be described by traditional transport theory with the configurational entropy properly quantified. Unlike most studies at mesoscopic level, this theory focuses on the macroscopic group behavior of DNA transportation. It is therefore easier to conduct validation analysis through comparison with experimental results. It is also promising in design and optimization of DNA filtration devices through computer simulation.

2007-01-01T00:00:00Z Nguyen, N. C. Peraire, Jaime https://hdl.handle.net/1721.1/35822 2019-04-12T08:35:47Z 2007-01-01T00:00:00Z

An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations Nguyen, N. C.; Peraire, Jaime In the presence of nonaffine and highly nonlinear terms in parametrized partial differential equations, the standard Galerkin reduced-order approach is no longer efficient, because the evaluation of these terms involves high computational complexity. An efficient reduced-order approach is developed to deal with “nonaffineness” and nonlinearity. The efficiency and accuracy of the approach are demonstrated on several test cases, which show significant computational savings relative to classical numerical methods and relative to the standard Galerkin reduced-order approach.

2007-01-01T00:00:00Z Tan, Alex Y.K. Patera, Anthony T. https://hdl.handle.net/1721.1/35808 2019-04-10T09:58:46Z 2007-01-01T00:00:00Z

Reduced Basis Method for 2nd Order Wave Equation: Application to One-Dimensional Seismic Problem Tan, Alex Y.K.; Patera, Anthony T. We solve the 2nd order wave equation, hyperbolic and linear in nature, for the pressure distribution of one-dimensional seismic problem with smooth initial pressure and rate of pressure change. The reduced basis method, offline-online computational procedures and a posteriori error estimation are developed. We show that the reduced basis pressure distribution is an accurate approximation to the finite element pressure distribution and the offline-online computational procedures work well. The a posteriori error estimation developed shows that the ratio of the maximum error bound over the maximum norm of the reduced basis error has a constant magnitude of O(10²). The inverse problem works well, giving a “possibility region” of a set of system parameters where the actual system parameters may reside.

2007-01-01T00:00:00Z Ali, S. Damodaran, Murali Willcox, Karen E. https://hdl.handle.net/1721.1/35781 2019-04-10T09:58:50Z 2007-01-01T00:00:00Z

Approximate Low Dimensional Models Based on Proper Orthogonal Decomposition for Black-Box Applications Ali, S.; Damodaran, Murali; Willcox, Karen E. Many industrial applications in engineering and science are solved using commercial engineering solvers that function as black-box simulation tools. Besides being time consuming and computationally expensive, the actual mathematical models and underlying structure of these problems are for most part unknown. This paper presents a method for constructing approximate low-dimensional models for such problems using the proper orthogonal decomposition (POD) technique. We consider a heat diffusion problem and a contamination transport problem, where the actual mathematical models are assumed to be unknown but numerical data in time are available so as to enable the formation of an ensemble of snapshots The POD technique is then used to produce a set of basis functions that spans the snapshot collection corresponding to each problem. The key idea is then to assume some functional form of the low-order model, and use the available snapshot data to perform a least squares fit in the POD basis coordinate system to determine the unknown model coefficients. Initial results based on this approximation method seem to hold some promise in creating a predictive low-order model, that is, one able to predict solutions not included in the original snapshot set. Some issues arising from this approximation method are also discussed in this paper.

2007-01-01T00:00:00Z