Operators can also act on vector fields or forms rather than scalar fields, e.g., divergence and curl operators (Tong et al., 2003). View chapter Chapter Linear Threshold Machines Machine Learning Book2018, Machine Learning Marco Gori Explore book 3.4.1 Gradient Descent In this section we ...
3.2.4Divergence, curl, and gradient Divergence, curl, and gradient are operations commonly used incontinuum mechanicsand physics for transforming tensor fields into other forms of tensor fields using partial derivatives. For example, divergence[62]is a tensor operator that produces tensor field giving...
faceDiv Divergence of a face variable→cell-centered variable edgeCurl Curl of a edge variable→face variable cellGrad Gradient of a cell-centered variable→face variable aveF2CC, aveN2CC, etc. Averaging operators (e.g. F→CC, takes values on faces and averages them to cell-centers) getIn...
where Div and Curl are, respectively, the divergence and curl operators with respect to x, associated with the undeformed configuration. 4.1. Spectral Invariants The total energy function requires the restriction 𝑊=𝑊(𝑎)(𝑼,𝒂,𝒌,𝒈,𝜌,𝑒)=𝑊(𝑎)(𝑸𝑼𝑸𝑇,𝑸𝒂...
where DivDiv and CurlCurl are, respectively, the divergence and curl operators with respect to x, associated with the undeformed configuration. 4.1. Spectral Invariants The total energy function requires the restriction 𝑊=𝑊(𝑎)(𝑼,𝒂,𝒌,𝒈,𝜌,𝑒)=𝑊(𝑎)(𝑸𝑼𝑸𝑇,...
(A26) Now, using the divergence theorem for Equation (A12) and minimum potential energy principle with Πext = q(x, y) δwdA B we obtain the Euler-Lagrange equation governing the minimization principle (A27) Mxx,xx + Mxy,xy + Myy,yy − Qxxx,xxx − Qxxy,xxy − Qxyy,xyy −...