Sentence examples for construct basis from inspiring English sources

We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element.

The next step is to construct basis matrices for projectors and projector products.

We then construct basis vectors ( p 0, q 0 ) in R n for the projectors P 0 and Q 0 with their inversion ( p 0 ∗, q 0 ∗ ) T, where p 0 T ∈ R n, n 0, q 0 T ∈ R n, k 0 and n = n 0 + k 0. Thus an index-1 electric network can be decoupled as: (3a).

We first construct basis vectors ( p 0, q 0 ) in R n with their inversion ( p 0 ∗, q 0 ∗ ) T for the projectors P 0 and Q 0, where p 0 ∈ R n, n 0, q 0 ∈ R n, k 0. For this case we have two possibilities depending on the spectrum of the matrix pencil ( E, A ). Here, we assume that the matrix pencil ( E, A ) of Equation (1) has at least one finite eigenvalue.

To obtain the basis functions, we use the idea from geometrical optics and construct the basis functions by using the leading order term in the asymptotic expansion.

We present a general framework to construct a basis and explore potential applications in isogeometric analysis.

The goal in this paper is to construct multiscale basis functions for both pressure and velocity.

After obtaining each class, POD and DEIM is applied to construct the basis vectors of the reduced subspace.

This new approach allows one to construct a basis for highly luminescent MCs that may be further modified to be adapted for applications such as optical imaging.

The time-varying poles of this system are required to construct appropriate basis functions.

The POD method is then applied to each of these matrices to construct a basis for projection.