Related papers: Reduced basis method for computational lithography
Image modeling and simulation are critical to extending the limits of leading edge lithography technologies used for IC making. Simultaneous source mask optimization (SMO) has become an important objective in the field of computational…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
In this work we combine the framework of the Reduced Basis method (RB) with the framework of the Localized Orthogonal Decomposition (LOD) in order to solve parametrized elliptic multiscale problems. The idea of the LOD is to split a high…
We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…
The accuracy of the reduced-order model (ROM) mainly depends on the selected basis. Therefore, it is essential to compute an appropriate basis with an efficient numerical procedure when applying ROM to nonlinear problems. In this paper, we…
We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parametrized by the…
Reduced order models, in particular the reduced basis method, rely on empirically built and problem dependent basis functions that are constructed during an off-line stage. In the on-line stage, the precomputed problem-dependent solution…
The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parametrized partial differential equations. We consider a quantity of interest, which is a linear…
We extend a localized model order reduction method for the distributed finite element solution of elliptic boundary value problems in the cloud. We give a computationally efficient technique to compute the required inner product matrices…
In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing…
In the realm of lithography, Optical Proximity Correction (OPC) is a crucial resolution enhancement technique that optimizes the transmission function of photomasks on a pixel-based to effectively counter Optical Proximity Effects (OPE).…
In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…
Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problems has been hindered by the…
This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the…
In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
We introduce a hyperreduced reduced basis element method for model reduction of parameterized, component-based systems in continuum mechanics governed by nonlinear partial differential equations. In the offline phase, the method constructs,…
This contribution presents a model order reduction framework for real-time efficient solution of trimmed, multi-patch isogeometric Kirchhoff-Love shells. In several scenarios, such as design and shape optimization, multiple simulations need…
The Reduced Basis Method (RBM) is a model reduction technique used to solve parametric PDEs that relies upon a basis set of solutions to the PDE at specific parameter values. To generate this reduced basis, the set of a small number of…
We present a reduced basis method for cheaply constructing (possibly rough) approximations to the nodal basis functions of the virtual element space, and propose to use such approximations for the design of the stabilization term in the…