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One of the important aspects of IsoGeometric Analysis (IGA) is the strong link between Computer Aided Design and analysis. Two of IGA'a major challenge are the assembly of patches (Constructive Solid Geometry geometries made of Boolean…
In this paper, we consider the iterative method of subspace corrections with random ordering. We prove identities for the expected convergence rate, which can provide sharp estimates for the error reduction per iteration. We also study the…
Motivated by large-scale optimization problems arising in the context of machine learning, there have been several advances in the study of asynchronous parallel and distributed optimization methods during the past decade. Asynchronous…
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
In this work, a simple and efficient dual iterative refinement (DIR) method is proposed for dense correspondence between two nearly isometric shapes. The key idea is to use dual information, such as spatial and spectral, or local and global…
Asynchronous tasks, when created with over-decomposition, enable automatic computation-communication overlap which can substantially improve performance and scalability. This is not only applicable to traditional CPU-based systems, but also…
Automatic Speech Recognition (ASR) systems are often optimized to work best for speakers with canonical speech patterns. Unfortunately, these systems perform poorly when tested on atypical speech and heavily accented speech. It has…
A method to combine two quantum error-correcting codes is presented. Even when starting with additive codes, the resulting code might be non-additive. Furthermore, the notion of the erasure space is introduced which gives a full…
Large language models frequently commit unrecoverable reasoning errors mid-generation: once a wrong step is taken, subsequent tokens compound the mistake rather than correct it. We introduce $\textbf{Latent Phase-Shift Rollback}$ (LPSR): at…
We propose a new, harmonically enriched multiscale coarse space (HEM) for domain decomposition methods. For a coercive high contrast model problem, we show how to enrich the coarse space so that the method is robust against any variations…
The growing demand for highly reliable communication systems drives the research and development of algorithms that identify and correct errors during data transmission and storage. This need becomes even more critical in hard-to-access or…
The impacts of channel estimation errors, inter-cell interference, phase adjustment cost, and computation cost on an intelligent reflecting surface (IRS)-assisted system are severe in practice but have been ignored for simplicity in most…
We consider composite linear inverse problems where the signal to recover is modeled as a sum of two functions. We study a variational framework formulated as an optimization problem over the pairs of components using two regularization…
The purpose of this paper is to study the influence of relaxation and acceleration techniques on the convergence behavior of the non-overlapping Schwarz algorithm with alternating Dirichlet-Neumann transmission conditions in the context of…
A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by…
Scaling inference-time computation has substantially improved the reasoning capabilities of language models. However, existing methods have significant limitations: serialized chain-of-thought approaches generate overly long outputs,…
In the present work, we study and analyze an efficient iterative coupling method for a dimensionally heterogeneous problem . We consider the case of 2-D Laplace equation with non symmetric boundary conditions with a corresponding 1-D…
In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite element methods of arbitrary polynomial degree $p \ge 0$ on…
In this chapter, we show how the use of differential coding and the presence of phase slips in the transmission channel affect the total achievable information rates and capacity of a system. By means of the commonly used QPSK modulation,…