Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fully Implicit Spectral Boundary Integral Computation of Red Blood Cell
  Flow   An approach is presented for implicit time integration in computations of red
blood cell flow by a spectral boundary integral method. The flow of a red cell
in ambient fluid is represented as a boundary integral equation (BIE), whose
structure is that of an implicit ordinary differential equation (IODE). The
cell configuration and velocity field are discretized with spherical harmonics.
The IODE is integrated in time using a multi-step implicit method based on
backward difference formulas, with variable order and adaptive time-stepping
controlled by local truncation error and convergence of Newton iterations.
Jacobians of the IODE, required for Newton's method, are implemented as
Jacobian matrix-vector products that are nothing but directional derivatives.
Their computation is facilitated by the weakly singular format of the BIE, and
these matrix-vector products themselves amount to computing a second BIE.
Numerical examples show that larger time steps are possible and that the number
of matrix-vector products is comparable to explicit methods.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
30
The categories of this paper are: q-alg