Gilbert Strang's research while affiliated with Massachusetts Institute of Technology and other places
What is this page?
This page lists the scientific contributions of an author, who either does not have a ResearchGate profile, or has not yet added these contributions to their profile.
It was automatically created by ResearchGate to create a record of this author's body of work. We create such pages to advance our goal of creating and maintaining the most comprehensive scientific repository possible. In doing so, we process publicly available (personal) data relating to the author as a member of the scientific community.
If you're a ResearchGate member, you can follow this page to keep up with this author's work.
If you are this author, and you don't want us to display this page anymore, please let us know.
It was automatically created by ResearchGate to create a record of this author's body of work. We create such pages to advance our goal of creating and maintaining the most comprehensive scientific repository possible. In doing so, we process publicly available (personal) data relating to the author as a member of the scientific community.
If you're a ResearchGate member, you can follow this page to keep up with this author's work.
If you are this author, and you don't want us to display this page anymore, please let us know.
Publications (9)
We study four problems, two in L1 and two in L∞, whose analogues in L2 are the familiar minimum principles which lead to the Laplace equation. One possibility is to be given the boundary value φ{symbol} = g and to minimize |vψ|1 or |v|∞; the gradient at a point (x,y) in Ω is measured by |vΔ |2 = ψ2x + ψ2y. In the other problems we are given a vecto...
In place of flows on a discrete network we study flows described by a vector field σ(x,y) in a plane domain ω. The analogue of the capacity constraint is |σ|≤c(x,y), and the strength of sources and sinks is σ·n=λf on the boundary and—div σ=λF in the interior. We show that the largest λ (the maximal flow) is determined by the minimal cut. As in the...
We study the space BD(), composed of vector functions u for which all components ij=1/2(u
i, j+u
j, i) of the deformation tensor are bounded measures. This seems to be the correct space for the displacement field in the problems of perfect plasticity. We prove that the boundary values of every such u are integrable; indeed their trace is in L
1 ()N...
The theory of perfect plasticity leads to an optimization problem with a vector unknown which closely resembles the scalar problem of minimal surfaces. A new formulation is proposed in which the boundary conditions are relaxed to an extent, since they remain present.
An algorithm is described which appears to give an efficient solution of nonlinear finite element equations. It is a quisi-Nowton method, and we compare it with some of the alternatives. Initial tests of its application to both material and geometric nonlinearities are discussed.
Citations
... This discussion builds on Theorem 1 from Strang [1982]. To build intuition, imagine a wall in X with a gap that is large enough for the robot to pass through without touching the wall. ...
... We can nevertheless work with p = 2 upon choosing a gradually varying jump within the dislocation core, from 0 to the Burgers vector, as done in [2] and considered next in Proposition 7. Moreover, the natural framework where (5.1) holds is the space SBD(Ω) of special functions with bounded deformation (this space was introduced in [36], see also [4,22,37]). The proposition below provides an interpretation of the kinematic variable E at the mesoscopic scale. ...
... This characterization seems to have first appeared in [32,Section 4]. The fact that the minimum in (6.3) is attained easily follows from the Direct Method in the Calculus of Variations. ...
Reference: Convex duality for principal frequencies
... Note now that the extreme points of the polytope defined by ΛB T u 1 ≤ 1 are multiples of the vectors whose elements are zeros and ones (see, for example, [20]). Thus, each extreme point must be of the form u = c Q e Q , where Q is a cut induced by some node set S ⊆ V according to (6), c Q ∈ R is a constant such that |c Q | = ¯ λ −1 Q , and e Q ∈ R n is a vector with the entries being [e Q ] i = 1 if node i ∈ S and [e Q ] i = 0 if i ∈ V \ S. ...
... The latter variational problem turns out to always have a minimizer w, thanks to a Rellich type compactness theorem in BD(Ω) (the space of fields such that Ew is a bounded measure), see Temam and Strang [1980]. ...
... The diameter of this filter is contingent upon the dominant wavelength in each iteration. As the final portion of the inversion scheme, a conjugate-gradient method is utilized to update the model parameters (Fletcher & Reeves, 1964;Matthies & Strang, 1979), with the step length determined by a quadratic interpolation (Tape et al., 2007). ...
... The 3D volume of the scan is denoted Ω(x) as a closed domain. As the model of segmentation is thought of as continuous flow in three dimensions [11,12] the source and sink terminal vertices are denoted as s and t. At every x ∈ Ω, p(x) is the passing, p s (x) the directed flow from source to the current position, p t (x) is the directed sink flow from x to t. ...
... which is finite for u ∈ BD(Ω; R d ), the space of vector fields of bounded deformation [35,36]. ...
