  In this thesis, we develop, discuss and implement algorithms for scalable
parallel tree-based adaptive mesh refinement (AMR) using space-filling curves
(SFCs). We create an AMR software that works independently of the used element
type, such as for example lines, triangles, tetrahedra, quadrilaterals,
hexahedra, and prisms. Along with a detailed mathematical discussion, this
requires the implementation as a numerical software and its validation, as well
as scalability tests on current supercomputers. For triangular and tetrahedral
elements (simplices) with red-refinement (1:4 in 2D, 1:8 in 3D), we develop a
new SFC index, the tetrahedral Morton index (TM-index). Its construction is
similar to the Morton index for quadrilaterals/hexahedra, as it is also based
on bitwise interleaving the coordinates of a certain vertex of the simplex, the
anchor node. We develop and demonstrate a new simplicial SFC and create a fast
and scalable tree-based AMR software that offers a flexibility and generality
that was previously not available.
