  An important ingredient of any moving-mesh method for fluid-structure
interaction (FSI) problems is the mesh deformation technique (MDT) used to
adapt the computational mesh in the moving fluid domain. An ideal technique is
computationally inexpensive, can handle large mesh deformations without
inverting mesh elements and can sustain an FSI simulation for extensive periods
ot time without irreversibly distorting the mesh. Here we compare several
commonly used techniques based on the solution of elliptic partial differential
equations, including harmonic extension, bi-harmonic extension and techniques
based on the equations of linear elasticity. Moreover, we propose a novel
technique which utilizes ideas from continuation methods to efficiently solve
the equations of nonlinear elasticity and proves to be robust even when the
mesh is subject to extreme deformations. In addition to that, we study how each
technique performs when combined with the Jacobian-based local stiffening. We
evaluate each technique on a popular two-dimensional FSI benchmark reproduced
by using an isogeometric partitioned solver with strong coupling.
