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Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver. [7] Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage. To avoid this expense, matrix-free methods are employed.
The Bogacki–Shampine method is implemented in the ode3 for fixed step solver and ode23 for a variable step solver function in MATLAB (Shampine & Reichelt 1997). Low-order methods are more suitable than higher-order methods like the Dormand–Prince method of order five, if only a crude approximation to the solution is required. Bogacki and ...
Kantorovich in 1948 proposed calculating the smallest eigenvalue of a symmetric matrix by steepest descent using a direction = of a scaled gradient of a Rayleigh quotient = (,) / (,) in a scalar product (,) = ′, with the step size computed by minimizing the Rayleigh quotient in the linear span of the vectors and , i.e. in a locally optimal manner.
In mathematics, more specifically in numerical linear algebra, the biconjugate gradient method is an algorithm to solve systems of linear equations A x = b . {\displaystyle Ax=b.\,} Unlike the conjugate gradient method , this algorithm does not require the matrix A {\displaystyle A} to be self-adjoint , but instead one needs to perform ...
Please help improve it to make it understandable to non-experts, without removing the technical details. ( May 2015 ) ( Learn how and when to remove this message ) In numerical linear algebra , the biconjugate gradient stabilized method , often abbreviated as BiCGSTAB , is an iterative method developed by H. A. van der Vorst for the numerical ...
The first SPIKE partitioning and algorithm was presented in and was designed as the means to improve the stability properties of a parallel Givens rotations-based solver for tridiagonal systems. A version of the algorithm, termed g-Spike, that is based on serial Givens rotations applied independently on each block was designed for the NVIDIA ...
The MLFMM is based on the Method of Moments (MoM), but reduces the memory complexity from () to (), and the solving complexity from () to (), where represents the number of unknowns and the number of iterations in the solver. This method subdivides the Boundary Element mesh into different clusters and if two clusters are in each other's ...
The state variables obtained after Step 2 are averaged over each cell defining a new piecewise constant approximation resulting from the wave propagation during the time interval . To be consistent, the time interval Δ t {\displaystyle {\Delta t}\,} should be limited such that the waves emanating from an interface do not interact with waves ...