Sentence examples for by the same basis from inspiring English sources

The geometry and field are usually approximated by the same basis functions in IGA, such as the B-spline or the NURBS basis functions.

In the same way the weighting coefficients of the second-order derivative are derived by the same basis functions and the weighting coefficients are found as [32] b i j = 2 a i j ( a i i − 1 x i − x j ), i, j = 1, 2, …, N, i ≠ j, (18).

The reconstruction polynomials in primitive variables are spanned by the same basis functions (psi_{r}(xi)) used for (mathbf{w}_{h}), hence mathbf{p}^{s,x}_{h}bigl x,t^{n} bigr) = sum_{r=0}^{M} psi_{r}( xi) hat{mathbf{p}} ^{n,s}_{ijk,r} := psi_{r}(xi) hat{mathbf{p}}^{n,s}_{ijk,r}.

The weak form of the constraint is obtained by utilising the same basis functions not only to represent geometry, response, and design variables, but also Lagrange multipliers.

This unification is brought about by employing the same basis functions to describe exact geometry and to approximate the physical response.

Isogeometric analysis (IGA) [18] is a method aimed at avoiding the discretization errors by using the same basis for analysis as is used to describe the geometry, thus enabling IGA to discretize the analysis models exactly.

They are inspected by Ofsted on the same basis as other schools, and their reports are on the Ofsted website.

The Přemyslid prince Vratislav II (1061 92) obtained from the Holy Roman emperor Henry IV the title of king of Bohemia as a personal (i.e., nonhereditary) privilege, and Prince Vladislav II (1140 73) was awarded the royal crown on the same basis by Emperor Frederick I Barbarossa.

A spokesman for the regulator commented: "We publish each of the PSB channels' spending on first-run, originated programming based on returns provided by each broadcaster, and on the same basis as all the previous PSB annual reports.

Each section is headed by a subchief, who is the eldest suitable descendant in the male line of the founder of the area; the chiefdom is headed by a paramount chief chosen on the same basis.

The court simply instructed the United States Court of Appeals for the Ninth Circuit to reconsider its ruling in light of the Supreme Court's decision in June to require access to public school buildings by after-school religious clubs on the same basis as any after-school activity.