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Article
Projection-Based Dimensional Reduction of Adaptively Refined Nonlinear Models
Adaptive mesh refinement (AMR) is fairly practiced in the context of high-dimensional, mesh-based computational models. However, it is in its infancy in that of low-dimensional, generalized-coordinate-based co...
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Article
A Practical Factorization of a Schur Complement for PDE-Constrained Distributed Optimal Control
A distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the ef...
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Article
Design optimization using hyper-reduced-order models
Solving large-scale PDE-constrained optimization problems presents computational challenges due to the large dimensional set of underlying equations that have to be handled by the optimizer. Recently, projecti...
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Chapter
On the Stability of Reduced-Order Linearized Computational Fluid Dynamics Models Based on POD and Galerkin Projection: Descriptor vs Non-Descriptor Forms
The Galerkin projection method based on modes generated by the Proper Orthogonal Decomposition (POD) technique is very popular for the dimensional reduction of linearized Computational Fluid Dynamics (CFD) mod...
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Chapter and Conference Paper
A Domain Decomposition Solver for the Discontinuous Enrichment Method for the Helmholtz Equation
The discontinuous enrichment method (DEM) [4] for the Helmholtz equation approximates the solution as a sum of a piecewise polynomial continuous function and element-wise supported plane waves [5]. A weak cont...
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Chapter and Conference Paper
Game Changing Computational Engineering Technology
During the last two decades, giant strides have been achieved in many aspects of Computational Engineering. Higher-fidelity mathematical models, better approximation methods, and faster algorithms have been de...
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Chapter and Conference Paper
Scalable FETI Algorithms for Frictionless Contact Problems
We review our FETI based domain decomposition algorithms for the solution of 2D and 3D frictionless contact problems of elasticity and related theoretical results. We consider both cases of restrained and unre...
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Chapter and Conference Paper
A FETI Method for a Class of Indefinite or Complex Second- or Fourth-Order Problems
The FETI-DP domain decomposition method is extended to address the iterative solution of a class of indefinite problems of the form (K − σ 2 M)x = b, and a class of...
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Chapter and Conference Paper
Dynamic-Data-Driven Real-Time Computational Mechanics Environment
The proliferation of sensor networks in various areas of technology has enabled real-time behavioral monitoring of various physical systems in various length and time scales. The opportunity to use these data ...
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Chapter and Conference Paper
Linear-Theory-Based Shape Optimization for Sonic Boom Minimization
An overpressure ground signature with more than two shocks is proposed for sonic boom minimization. A procedure coupling linear-theory-based sonic boom theory with a state-of-the-art optimization tool is prese...
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Chapter and Conference Paper
On the Solution of Inverse Obstacle Acoustic Scattering Problems with a Limited Aperture
We present a computational methodology for retrieving the shape of a rigid obstacle from the knowledge of some acoustic far-field patterns. This methodology is based on the well-known regularized Newton algori...
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Chapter and Conference Paper
DDEMA: A Data Driven Environment for Multiphysics Applications
In this paper we present the design of a multidisciplined problem solving environment (MPSE) for supporting an efficient prediction capability for the response of multiscale interdisciplinary continuous intera...
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Chapter and Conference Paper
A Blended Fictitious/Real Domain Decomposition Method for Partially Axisymmetric Exterior Helmholtz Problems with Dirichlet Boundary Conditions
We blend a fictitious domain decomposition method and the FETI-H substructuring algorithm to construct a fast finite element based solver for exterior Helmholtz problems characterized by partially axisymmetric...
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Article
A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems
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Article
Solution of finite element systems on concurrent processing computers
A new computer program architecture for the solution of finite element systems using concurrent processing is presented. The basic approach involves the automatic creation of substructures. A host provides con...
