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This scheme uses only the value and first-order derivatives of the physical field as computational variables, and thus largely reduces the memory requirement.
The higher-order cross derivatives are not treated as the computational variables but calculated by recursively using the local Taylor expansions within each single mesh cell, which retains the third order accuracy even for meshes of non-uniform grid spacings.
Differently from conventional FVM where the volume integrated average (VIA) value is the only computational variable, the present formulation treats both VIA and the point value (PV) as the computational variables which are updated separately at each time step.
In the present model, all unknowns or computational variables are point values and no numerical quadrature is involved, which particularly benefits the computational accuracy and efficiency in handling the spherical geometry, such as coordinate transformation and curved surface.
The VPM method treats two different discretized moments of the physical fields, i.e. the volume integrated average (VIA) and the point values (PV) at the vertices of each cell, as the computational variables, which distinguishes it from conventional FVM.
The function (u x,t)) in physical variables can be transformed into the function in computational variables u x,t)=ubigl(x xi,t),tbigr), and the blow-up profile is expressed in the computational variable ξ.
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The left is the moving mesh (x xi,t)) and the right is the blow-up profiles in the computational variable ξ. Figure 2 The blow-up profiles for (pmb{p=5}) in Example 5.2.
On the other hand, fine-tuning of the computational variable, i.e. the gene interaction network, proved more critical for accurate predictions of single gene drug targets.
The goal of this study was to improve our understanding of the interaction between biological testing and computational training variables in order to produce more accurate predictions of drug action at the transcriptional level.
Finally, with the aid of recently available computational tools, variables (e.g., flow fields of a particular bioreactor design [ 117, 118], incorporation of the mechanics of the scaffold material [ 119], and the sufficiency of bioreactor cultures [ 117, 120, 121], shear stresses and mass transfer in scaffold-containing bioreactors [ 118, 122]) can be estimated.
As compared to conventional finite-difference time-domain methods, an important advantage of the proposed algorithm is a dynamical control of accuracy: Variable time steps or variable computational costs per time step with error control are possible.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com