Acquisitions (Details Textual) $ in Thousands	12 Months Ended
	Dec. 31, 2022 USD ($) acquisition	Jan. 01, 2022 USD ($)	Jan. 02, 2021 USD ($)	Aug. 31, 2022 USD ($)	Jul. 14, 2022 USD ($)	Apr. 14, 2021 USD ($)	Feb. 23, 2021 USD ($)
Business Acquisition [Line Items]
Cash consideration to acquire businesses, net of cash acquired	$ 613,785	$ 226,201	$ 197,562
Goodwill	1,374,268	928,358	782,087
Transaction costs associated with acquisitions	10,100	2,600	2,400
OpenEye Scientific Software, Inc.
Business Acquisition [Line Items]
Cash consideration to acquire businesses, net of cash acquired	$ 461,300
Cash acquired				$ 13,200
Goodwill				359,580
Acquired intangibles				$ 117,400
Acquired definite-lived intangible assets, weighted average useful life	9 years 9 months 18 days
OpenEye Scientific Software, Inc. | Existing Technology [Member]
Business Acquisition [Line Items]
Acquired definite-lived intangible assets, weighted average useful life	7 years
OpenEye Scientific Software, Inc. | Agreements and Relationship [Member]
Business Acquisition [Line Items]
Acquired definite-lived intangible assets, weighted average useful life	12 years 3 months 18 days
OpenEye Scientific Software, Inc. | Tradename Trademark and Patents [Member]
Business Acquisition [Line Items]
Acquired definite-lived intangible assets, weighted average useful life	7 years
FFG Holdings Limited ("Future Facilities")
Business Acquisition [Line Items]
Cash consideration to acquire businesses, net of cash acquired	$ 100,100
Cash acquired					$ 2,800
Goodwill					67,219
Acquired intangibles					$ 38,100
Acquired definite-lived intangible assets, weighted average useful life	7 years 3 months 18 days
FFG Holdings Limited ("Future Facilities") | Existing Technology [Member]
Business Acquisition [Line Items]
Acquired definite-lived intangible assets, weighted average useful life	6 years
FFG Holdings Limited ("Future Facilities") | Agreements and Relationship [Member]
Business Acquisition [Line Items]
Acquired definite-lived intangible assets, weighted average useful life	9 years
FFG Holdings Limited ("Future Facilities") | Tradename Trademark and Patents [Member]
Business Acquisition [Line Items]
Acquired definite-lived intangible assets, weighted average useful life	8 years
2022 Other business combination
Business Acquisition [Line Items]
Cash consideration to acquire businesses, net of cash acquired	$ 53,600
Goodwill	29,500
Acquired intangibles	$ 23,100
Acquired definite-lived intangible assets, weighted average useful life	6 years 10 months 24 days
Number of businesses acquired | acquisition	3
Goodwill, expected to be tax deductible	$ 27,800
2022 Other business combination | Existing Technology [Member]
Business Acquisition [Line Items]
Acquired intangibles assets with finite lives	13,100
2022 Other business combination | Agreements and Relationship [Member]
Business Acquisition [Line Items]
Acquired intangibles assets with finite lives	3,100
2022 Other business combination | Tradename Trademark and Patents [Member]
Business Acquisition [Line Items]
Acquired intangibles assets with finite lives	100
2022 Other business combination | In-process technology
Business Acquisition [Line Items]
Acquired intangible assets with infinite lives	$ 6,800
NUMECA
Business Acquisition [Line Items]
Cash consideration to acquire businesses, net of cash acquired		188,600
Cash acquired							$ 9,600
Goodwill							133,077
Acquired intangibles							$ 72,200
Pointwise
Business Acquisition [Line Items]
Cash consideration to acquire businesses, net of cash acquired		$ 31,400
Goodwill						$ 16,700
Acquired intangibles						$ 16,700
AWR and Integrand
Business Acquisition [Line Items]
Cash consideration to acquire businesses, net of cash acquired			195,600
Cash acquired			1,500
Goodwill			119,400
Acquired intangibles			$ 101,300
Acquired definite-lived intangible assets, weighted average useful life			9 years
Net other identifiable assets and liabilities resulting from acquisitions			$ (25,100)