Related papers: Automatic implementation of material laws: Jacobia…
This paper presents a new functionality of the Automatic Differentiation (AD) tool Tapenade. Tapenade generates adjoint codes which are widely used for optimization or inverse problems. Unfortunately, for large applications the adjoint code…
This paper proposes a new methodology for deriving a point-based dimensionally homogeneous Jacobian, intended for performance evaluation and optimization of parallel manipulators with mixed degrees of freedom. Optimal manipulator often rely…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
An effective numerical method is presented for optimizing model parameters that can be applied to any type of system of non-linear equations and any number of data-points, which does not require explicit formulation of the objective…
Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…
Matched layers are commonly used in numerical simulations of wave propagation to model (semi-)infinite domains. Attenuation functions describe the damping in layers, and provide a matching of the wave impedance at the interface between the…
We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilateral, hexahedral and triangular prismatic cells. The algebra…
We propose a gradient-based Jacobi algorithm for a class of maximization problems on the unitary group, with a focus on approximate diagonalization of complex matrices and tensors by unitary transformations. We provide weak convergence…
This paper presents a novel framework for Jacobian computation in motion optimization problems involving multi-link systems, where physical quantities are represented using higher-order time derivatives. In motion optimization of robots and…
In this paper, we develop a fully discrete Galerkin method for solving initial value fractional integro-differential equations(FIDEs). We consider Generalized Jacobi polynomials(GJPs) with indexes corresponding to the number of homogeneous…
We present a relative forward error analysis of a mixed-precision preconditioned one-sided Jacobi algorithm, analogous to a two-sided version introduced in [N. J. Higham, F. Tisseur, M. Webb and Z. Zhou, SIAM J. Matrix Anal. Appl. 46…
A program RCFP will be presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. The list of quantities wich are supported by the present program includes the…
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…
Tensor analysis provides a frame-invariant foundation for continuum mechanics, yet numerical implementations rely on matrix representations expressed in user-selected bases. When these bases are non-Cartesian and non-orthonormal, additional…
We present a framework to solve non-linear eigenvalue problems suitable for a Finite Element discretization. The implementation is based on the open-source finite element software GetDP and the open-source library SLEPc. As template…
In this paper, a topology optimization framework utilizing automatic differentiation is presented as an efficient way for solving 2D density-based topology optimization problem by calculating gradients through the fully differentiable…
Singular equations with rank-deficient Jacobians arise frequently in algebraic computing applications. As shown in case studies in this paper, direct and intuitive modeling of algebraic problems often results in nonisolated singular…
The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order…
We describe a suite of fast algorithms for evaluating Jacobi polynomials, applying the corresponding discrete Sturm-Liouville eigentransforms and calculating Gauss-Jacobi quadrature rules. Our approach is based on the well-known fact that…
An efficient method is proposed for computing the structure of Jordan blocks of a matrix of integers or rational numbers by exact computation. We have given a method for computing Jordan chains of a matrix with exact computation. However,…