Non-intrusive approaches for the construction of computational vademecums face different challenges, especially when a parameter variation affects the physics of the problem considerably. In these situations, classical interpolation becomes inaccurate. Therefore, classical approaches for the construction of an offline computational vademecum, typically by using model reduction techniques, are no longer valid. Such problems are faced in different physical simulations, for example welding path problems, resin transfer molding, or sheet compression molding, among others. In such situations, the interpolation of precomputed solutions at prescribed parameter values (built using either intrusive or non intrusive techniques) generates spurious numerical artifacts. In this work, we propose an alternative interpolation and simulation strategy by using physically-based morphing of spaces. The morphing will transform the uncompatibe physical domains of the problem’s solution into a compatible one, where an interpolation free of artifacts can be performed. Later on, an inverse transformation can be used to push-back the solution. Different relevant examples are illustrated in this work to motivate the use of the proposed method.

用于构造计算变量的非侵入式方法面临着不同的挑战，特别是当参数变化对问题的物理性产生重大影响时。在这些情况下，经典插值变得不准确。因此，通常通过使用模型归约技术来构造脱机计算变量的经典方法不再有效。这些问题在不同的物理模拟中面临，例如焊接路径问题，树脂传递模塑或片材压缩模塑等。在这种情况下，以指定的参数值（使用介入式或非介入式技术构建）对预先计算的解进行插值会生成伪造的数值假象。在这项工作中 我们通过使用基于物理的空间变形提出了一种替代的插值和模拟策略。变形会将问题解决方案的不兼容物理域转换为兼容域，在其中可以执行没有伪像的插值。稍后，可以使用逆变换来推回解决方案。在这项工作中说明了不同的相关示例，以激发所提出方法的使用。