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14 ore fa · Abstract. Poroelastic models describe a coupled solid-fluid interaction between a solid skeleton saturated by some fluid. We consider Biot’s model that describes the deformation of the solid skeleton by linear elasticity and the fluid flow by Darcy’s law. The formulation includes displacements, fluid flux and fluid pressure.
14 ore fa · The biggest calculation that the full-grid solver can run has about \(2.6\times 10^5\) degrees of freedom, while the biggest calculation that the tensor-train solver can run has about \(8.6\times 10^9\) degrees of freedom.
14 ore fa · We use the Alternating Minimal Energy method (AME) to acquire the TT approximation of the solution for linear equation systems, as proposed in . In the context of the solution to the reduced problem, all segments of the system matrix’s canonical form are minimal.
14 ore fa · This means that numerically solving anomalous diffusion problems is computationally expensive. In the general case solving a dense system of linear algebraic equations has computational complexity of \(O(N^3)\). If K can be sparsified (approximated by a sparse matrix), then computationally cheaper specialized direct methods can be used.
14 ore fa · Experimental data were fitted in a least squares fashion using an ordinary differential equation (ODE) solver. Glycolytic rate constants (k gl) were multiplied by the number of moles of glucose added, and normalised to cell number, and cell volume (Supplementary Fig. S1) to give glycolytic flux in units of mol (total cell volume) −1 s −1.
14 ore fa · Free Online Scientific Notation Calculator. Solve advanced problems in Physics, Mathematics and Engineering. Math Expression Renderer, Plots, Unit Converter, Equation Solver, Complex Numbers, Calculation History.
14 ore fa · Some of the biggest problems solved at present contain more than 200 000 000 ordinary differential equations. Moreover, in the case of studying air pollution problems, one can solve such systems of equations hundred thousand time steps and even bigger computational tasks in a comprehensive study related to future climate changes and high pollution levels.
